Regularization of w: Simulated True Effects with Homoscedastic Correlated Noises

Last updated: 2017-05-16

Code version: cbce2c8

Introduction

Similar to previous simulations, where correlated null \(z\) scores are fitted by \(10\) Gaussian derivatives with regularization, we are now fitting data sets simulated with correlated noise and true signals by both ASH and Gaussian derivatives using the same regularization and see what happens.

The model

\[ \begin{array}{c} \beta_j \sim g = \sum\limits_{k=0}^K\pi_kg_k \ ;\\ g \text{ is unimodal} \ ; \\ \hat\beta_j | \beta_j, \hat s_j = \beta_j + \hat s_jz_j \ ;\\ z_j \sim N(0, 1) \text{, marginally} \ ; \\ z_j \text{ correlated} \ . \end{array} \] ## Fitting the model

\[ \begin{array}{rl} \min\limits_{\pi,w} & -\sum\limits_{j = 1}^n\log \left(\sum\limits_{k = 0}^K\sum\limits_{l=1}^L\pi_k w_l f_{jkl} + \sum\limits_{k = 0}^K\pi_kf_{jk0}\right) - \sum\limits_{k = 0}^K\left(\lambda_k^\pi - 1\right)\log\left(\pi_k\right) + \sum\limits_{l = 1}^L\lambda_l^w\left|w_l\right| \\ \text{subject to} & \sum\limits_{k = 0}^K\pi_k = 1 \ ;\\ & \pi_k \geq 0 \ .\\ \end{array} \] where \(f_{jkl}\) have an analytic form for both \(g_k\) being normal and uniform, and should be normalized.

Uniform mixture prior

\[ \begin{array}{rrcl} &\beta_j &\sim & \sum_k \pi_k \text{ Unif }[a_k, b_k]\\ \Rightarrow & f_{jkl} &= & \displaystyle\frac{\varphi^{(l-1)}\left(\frac{\hat\beta_j-a_k}{\hat s_j}\right) - \varphi^{(l-1)}\left(\frac{\hat\beta_j-b_k}{\hat s_j}\right)}{\sqrt{l!}\left(b_k - a_k\right)} \ . \end{array} \]

Normal mixture prior

\[ \begin{array}{rrcl} &\beta_j &\sim & \sum_k \pi_k N\left(\mu_k, \sigma_k^2\right) \\ \Rightarrow & f_{jkl} &= & \displaystyle\frac{\hat s_j^l}{\sqrt{l!}\left(\sqrt{\sigma_k^2 + \hat s_j^2}\right)^{l+1}} \varphi^{(l)}\left(\frac{ \hat\beta_j - \mu_k }{ \sqrt{\sigma_k^2 + \hat s_j^2} }\right) \ . \end{array} \]

In the following simulation, the parameters are set in the following way.

\(K\) is chosen by the default function in ashr.
The prior mixture always include a point mass at \(0\); that is, \(g_0 = \delta_0\).
The estimate of \(g\) is biased against underestimating \(\hat\pi_0\), by setting \(\lambda_0^\pi = 10\), \(\lambda_k^\pi = 1\), \(k \geq 1\). The previous two are implemented by setting method = "fdr".
Only even-order \(w_l\) are regularized, and the odd-order \(w_l\) are encouraged to decay in the order of \(\rho^{l / 2}\), for some \(\rho\in\left(0, 1\right)\). For even orders, \(\lambda_l^w = \lambda / \rho^{l / 2}\); for odd orders, \(\lambda_l^w = 0\).
The parameters are set as \(L = 10\), \(\lambda = 10\), \(\rho = 0.5\).

library(ashr)
source("../code/gdash.R")

L = 10
lambda = 10
rho = 0.5

The data

The data are simulated on top of the real correlated null \(z\) scores in three steps.

The true signals \(\beta_j\) are simulated from four kinds of \(g\), the global null \(g_n\), small effects \(g_s\), medium effects \(g_m\), and large effects \(g_l\).

\[ \begin{array}{rcl} g_n &=& \delta_0\\ g_s &=& 0.6\delta_0 + 0.3N\left(0, 1\right) + 0.1N\left(0, 2^2\right)\\ g_m &=& 0.6\delta_0 + 0.3N\left(0, 2\right) + 0.1N\left(0, 4^2\right)\\ g_l &=& 0.6\delta_0 + 0.3N\left(0, 3\right) + 0.1N\left(0, 6^2\right)\\ \end{array} \]

g.null = normalmix(pi = 1, mean = 0, sd = 0)
g.s.n = normalmix(pi = c(0.6, 0.3, 0.1), mean = 0, sd = c(0, 1, 2))
g.m.n = normalmix(pi = c(0.6, 0.3, 0.1), mean = 0, sd = c(0, 2, 4))
g.l.n = normalmix(pi = c(0.6, 0.3, 0.1), mean = 0, sd = c(0, 3, 6))

\(\hat s_j^2\) are either constant \(1\) or simulated from \(\chi_1^2\). Right now we are only working on the homoscedastic \(\hat s_j^2 \equiv 1\) case.

se = "constant"

With selected data sets of correlated null \(z\) scores, obtain \(\hat\beta_j = \beta_j + \hat s_j z_j\). These selected data sets are put into four categories: typical, hostile, friendly, iid.

Now we are fitting the model to these data sets, which contain simulated, known true signals, as well as noises with real, unknown correlations.

z.list = readRDS("../output/z_null_liver_777_select.RDS")
z.index = readRDS("../output/z_null_liver_777_select_index.RDS")

Category I: Typical

label = "typical"

Global null \(g_n\)

g = g.null

Data Set 32 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 3 ;
pihat0 by ASH: 0.184423 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 9.787 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 327 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 489 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1446 ;
pihat0 by ASH: 0.1522796 ;
Number of iterations: 35 ;
Converged: TRUE ;
Time: 82.747 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03531 ; 2 - 0.56098 ; 3 - -0.43402 ; 4 - 0 ; 5 - -0.19559 ; 6 - 0 ; 7 - 0.04624 ; 8 - 0 ; 9 - -0.04255 ; 10 - 0 ;

Data Set 355 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 639 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 2300 ;
pihat0 by ASH: 0.04750946 ;
Number of iterations: 14 ;
Converged: TRUE ;
Time: 32.32 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01381 ; 2 - 1.16994 ; 3 - 0.00537 ; 4 - 0.55234 ; 5 - -0.29768 ; 6 - 0 ; 7 - -0.53075 ; 8 - 0 ; 9 - -0.25584 ; 10 - 0 ;

Data Set 483 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9998824 ;
Number of iterations: 910 ;
Converged: TRUE ;
Time: 2314.257 Seconds;
Normalized w: 0 - 1 ; 1 - 13.62283 ; 2 - -7.083 ; 3 - 98.11621 ; 4 - -20.77466 ; 5 - 293.86947 ; 6 - -24.81337 ; 7 - 407.36442 ; 8 - 0 ; 9 - 216.65147 ; 10 - 0 ;

Data Set 778 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 357 ;
pihat0 by ASH: 0.07619716 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 6.173 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Small effects \(g_s\)

g = g.s.n

Data Set 32 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 3 ;
pihat0 by ASH: 0.184423 ;
Number of iterations: 16 ;
Converged: TRUE ;
Time: 42.727 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03028 ; 2 - 0.35574 ; 3 - 0.00706 ; 4 - -0.02919 ; 5 - 0.03751 ; 6 - 1e-05 ; 7 - 0.08977 ; 8 - 0 ; 9 - 0.03491 ; 10 - 0 ;

Data Set 327 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 489 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1446 ;
pihat0 by ASH: 0.1522796 ;
Number of iterations: 28 ;
Converged: TRUE ;
Time: 81.142 Seconds;
Normalized w: 0 - 1 ; 1 - 0.04 ; 2 - 0.51041 ; 3 - -0.43816 ; 4 - 0 ; 5 - -0.1971 ; 6 - 0 ; 7 - -0.12318 ; 8 - 0 ; 9 - -0.09824 ; 10 - 0 ;

Data Set 355 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 639 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 2300 ;
pihat0 by ASH: 0.04750946 ;
Number of iterations: 5000 ;
Converged: FALSE ;
Time: 14693.29 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01332 ; 2 - 1.10006 ; 3 - -0.01938 ; 4 - 0.46208 ; 5 - -0.41244 ; 6 - -1e-05 ; 7 - -0.67833 ; 8 - 0 ; 9 - -0.2834 ; 10 - 0 ;

Data Set 483 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9998824 ;
Number of iterations: 5000 ;
Converged: FALSE ;
Time: 14144.58 Seconds;
Normalized w: 0 - 1 ; 1 - 0.05386 ; 2 - -0.00086 ; 3 - 0.0993 ; 4 - 0.11038 ; 5 - 0.049 ; 6 - 0 ; 7 - 0.07738 ; 8 - 0 ; 9 - 0.04504 ; 10 - 0 ;

Data Set 778 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 357 ;
pihat0 by ASH: 0.07619716 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 42.477 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00546 ; 2 - 0.45141 ; 3 - -0.06237 ; 4 - 0 ; 5 - -4e-04 ; 6 - 0 ; 7 - -0.02274 ; 8 - 0 ; 9 - -0.05261 ; 10 - 0 ;

Medium effects \(g_m\)

g = g.m.n

Data Set 32 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 3 ;
pihat0 by ASH: 0.184423 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 56.929 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03333 ; 2 - 0.30388 ; 3 - -0.01338 ; 4 - -0.0554 ; 5 - -0.16216 ; 6 - 2e-05 ; 7 - -0.20437 ; 8 - 0 ; 9 - -0.12118 ; 10 - 0 ;

Data Set 327 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 489 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1446 ;
pihat0 by ASH: 0.1522796 ;
Number of iterations: 5001 ;
Converged: FALSE ;
Time: 16264.64 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01846 ; 2 - 0.52106 ; 3 - -0.69792 ; 4 - 0 ; 5 - -0.89705 ; 6 - 0 ; 7 - -0.76514 ; 8 - 0 ; 9 - -0.3562 ; 10 - 0 ;

Data Set 355 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 639 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 2300 ;
pihat0 by ASH: 0.04750946 ;
Number of iterations: 23 ;
Converged: TRUE ;
Time: 62.962 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03295 ; 2 - 0.89814 ; 3 - 0.08885 ; 4 - 1e-05 ; 5 - -0.25975 ; 6 - -1e-05 ; 7 - -0.40985 ; 8 - 0 ; 9 - -0.1112 ; 10 - 0 ;

Data Set 483 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9998824 ;
Number of iterations: 25 ;
Converged: TRUE ;
Time: 68.624 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02584 ; 2 - -0.08791 ; 3 - -0.09764 ; 4 - 0.08983 ; 5 - -0.37227 ; 6 - -1e-05 ; 7 - -0.39177 ; 8 - 0 ; 9 - -0.19974 ; 10 - 0 ;

Data Set 778 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 357 ;
pihat0 by ASH: 0.07619716 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 57.331 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01578 ; 2 - 0.43421 ; 3 - -0.06533 ; 4 - 1e-05 ; 5 - -0.13096 ; 6 - -1e-05 ; 7 - -0.10166 ; 8 - 0 ; 9 - -0.07965 ; 10 - 0 ;

Large effects \(g_l\)

g = g.l.n

Data Set 32 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 3 ;
pihat0 by ASH: 0.184423 ;
Number of iterations: 14 ;
Converged: TRUE ;
Time: 38.406 Seconds;
Normalized w: 0 - 1 ; 1 - -0.06374 ; 2 - 0.28062 ; 3 - -0.0511 ; 4 - -0.11532 ; 5 - -0.16729 ; 6 - 3e-05 ; 7 - -0.25316 ; 8 - 0 ; 9 - -0.16938 ; 10 - 0 ;

Data Set 327 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 489 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1446 ;
pihat0 by ASH: 0.1522796 ;
Number of iterations: 24 ;
Converged: TRUE ;
Time: 68.257 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00246 ; 2 - 0.51091 ; 3 - -0.80563 ; 4 - 1e-05 ; 5 - -1.11321 ; 6 - -1e-05 ; 7 - -0.69755 ; 8 - 0 ; 9 - -0.22284 ; 10 - 0 ;

Data Set 355 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 639 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 2300 ;
pihat0 by ASH: 0.04750946 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 49.838 Seconds;
Normalized w: 0 - 1 ; 1 - 0.04881 ; 2 - 0.88338 ; 3 - 0.16308 ; 4 - 1e-05 ; 5 - -0.36692 ; 6 - -1e-05 ; 7 - -1.0037 ; 8 - 0 ; 9 - -0.48371 ; 10 - 0 ;

Data Set 483 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9998824 ;
Number of iterations: 24 ;
Converged: TRUE ;
Time: 66.637 Seconds;
Normalized w: 0 - 1 ; 1 - 0.04712 ; 2 - -0.22017 ; 3 - 0.02326 ; 4 - 0.04457 ; 5 - -0.00417 ; 6 - -1e-05 ; 7 - 0.09157 ; 8 - 0 ; 9 - 0.05507 ; 10 - 0 ;

Data Set 778 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 357 ;
pihat0 by ASH: 0.07619716 ;
Number of iterations: 17 ;
Converged: TRUE ;
Time: 47.521 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02782 ; 2 - 0.41227 ; 3 - 0.14056 ; 4 - 2e-05 ; 5 - 0.52279 ; 6 - -1e-05 ; 7 - 0.72455 ; 8 - 0 ; 9 - 0.39068 ; 10 - 0 ;

Category II: Hostile

label = "hostile"

Global null \(g_n\)

g = g.null

Data Set 355 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 639 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 2300 ;
pihat0 by ASH: 0.04750946 ;
Number of iterations: 14 ;
Converged: TRUE ;
Time: 33.835 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01381 ; 2 - 1.16994 ; 3 - 0.00537 ; 4 - 0.55234 ; 5 - -0.29768 ; 6 - 0 ; 7 - -0.53075 ; 8 - 0 ; 9 - -0.25584 ; 10 - 0 ;

Data Set 23 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 408 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 2448 ;
pihat0 by ASH: 0.03139009 ;
Number of iterations: 9 ;
Converged: TRUE ;
Time: 23.769 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01619 ; 2 - 1.31213 ; 3 - 0.08603 ; 4 - 0.68475 ; 5 - 0.14676 ; 6 - 0 ; 7 - 0.09827 ; 8 - 0 ; 9 - 0.05365 ; 10 - 0 ;

Data Set 122 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 331 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1822 ;
pihat0 by ASH: 0.04301549 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.623 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 749 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 114 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1685 ;
pihat0 by ASH: 0.02583276 ;
Number of iterations: 9 ;
Converged: TRUE ;
Time: 19.872 Seconds;
Normalized w: 0 - 1 ; 1 - 0.04774 ; 2 - 1.03556 ; 3 - 0.00373 ; 4 - 0.41515 ; 5 - -0.02069 ; 6 - 0 ; 7 - 0.10887 ; 8 - 0 ; 9 - 0.10382 ; 10 - 0 ;

Data Set 724 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 79 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1814 ;
pihat0 by ASH: 0.01606004 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.055 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 56 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 35 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1137 ;
pihat0 by ASH: 0.04829662 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 32.224 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01514 ; 2 - 0.83799 ; 3 - 0.138 ; 4 - 0.29933 ; 5 - 0.19853 ; 6 - 0 ; 7 - 0.05111 ; 8 - 0 ; 9 - -0.04564 ; 10 - 0 ;

Data Set 840 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 28 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1653 ;
pihat0 by ASH: 0.02316832 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.93 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 858 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 16 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1506 ;
pihat0 by ASH: 0.05110069 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.058 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 771 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 12 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 795 ;
pihat0 by ASH: 0.04316169 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.264 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 389 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 11 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1028 ;
pihat0 by ASH: 0.03156173 ;
Number of iterations: 10 ;
Converged: TRUE ;
Time: 27.633 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00898 ; 2 - 0.80297 ; 3 - 0.18296 ; 4 - 0.23615 ; 5 - 0.1184 ; 6 - -0.02598 ; 7 - -0.0577 ; 8 - 0 ; 9 - -0.03478 ; 10 - 0 ;

Data Set 485 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 9 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 614 ;
pihat0 by ASH: 0.04794909 ;
Number of iterations: 5002 ;
Converged: FALSE ;
Time: 13143.21 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01252 ; 2 - 0.67521 ; 3 - 0.10748 ; 4 - 0.1333 ; 5 - 0.10225 ; 6 - -0.04329 ; 7 - -0.06145 ; 8 - 0 ; 9 - -0.05754 ; 10 - 0 ;

Data Set 77 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 7 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1307 ;
pihat0 by ASH: 0.05151585 ;
Number of iterations: 3 ;
Converged: TRUE ;
Time: 9.182 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02499 ; 2 - 0.88028 ; 3 - 0.35466 ; 4 - 0.33104 ; 5 - 0.21981 ; 6 - 0 ; 7 - -0.17464 ; 8 - 0 ; 9 - -0.14809 ; 10 - 0 ;

Data Set 984 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 7 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 689 ;
pihat0 by ASH: 0.04567195 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.909 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 360 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 6 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1392 ;
pihat0 by ASH: 0.0308234 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 47.276 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03954 ; 2 - 0.94125 ; 3 - 0.12507 ; 4 - 0.14723 ; 5 - 0.11351 ; 6 - -0.15806 ; 7 - -0.11173 ; 8 - 0 ; 9 - -0.11794 ; 10 - 0 ;

Data Set 522 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 4 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1149 ;
pihat0 by ASH: 0.02083846 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 46.947 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00643 ; 2 - 0.82031 ; 3 - -0.04252 ; 4 - 0 ; 5 - -0.07732 ; 6 - -0.17804 ; 7 - -0.09134 ; 8 - 0.04629 ; 9 - -0.09283 ; 10 - 0 ;

Data Set 22 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 508 ;
pihat0 by ASH: 0.03271534 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 6.156 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 269 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 662 ;
pihat0 by ASH: 0.02787007 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.962 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 403 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 227 ;
pihat0 by ASH: 0.0531628 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 6.17 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 923 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1340 ;
pihat0 by ASH: 0.03239883 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.93 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 3 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 193 ;
pihat0 by ASH: 0.0465218 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.688 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Small effects \(g_s\)

g = g.s.n

Data Set 355 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 639 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 2300 ;
pihat0 by ASH: 0.04750946 ;
Number of iterations: 19 ;
Converged: TRUE ;
Time: 50.662 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03213 ; 2 - 0.91844 ; 3 - 0.06692 ; 4 - 1e-05 ; 5 - 0.09274 ; 6 - 0 ; 7 - 0.55608 ; 8 - 0 ; 9 - 0.51084 ; 10 - 0 ;

Data Set 23 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 408 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 2448 ;
pihat0 by ASH: 0.03139009 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 46.01 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02179 ; 2 - 1.21742 ; 3 - 0.04752 ; 4 - 0.56253 ; 5 - 0.00067 ; 6 - 0 ; 7 - -0.14122 ; 8 - 0 ; 9 - -0.03517 ; 10 - 0 ;

Data Set 122 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 331 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1822 ;
pihat0 by ASH: 0.04301549 ;
Number of iterations: 28 ;
Converged: TRUE ;
Time: 74.447 Seconds;
Normalized w: 0 - 1 ; 1 - 0.0057 ; 2 - 0.72851 ; 3 - -0.22489 ; 4 - 0 ; 5 - 0.65686 ; 6 - 0 ; 7 - 1.05383 ; 8 - 0 ; 9 - 0.19799 ; 10 - 0 ;

Data Set 749 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 114 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1685 ;
pihat0 by ASH: 0.02583276 ;
Number of iterations: 19 ;
Converged: TRUE ;
Time: 49.791 Seconds;
Normalized w: 0 - 1 ; 1 - 0.04463 ; 2 - 0.78807 ; 3 - -0.04714 ; 4 - 0 ; 5 - -0.13858 ; 6 - 0 ; 7 - -0.14389 ; 8 - 0 ; 9 - 0.00443 ; 10 - 0 ;

Data Set 724 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 79 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1814 ;
pihat0 by ASH: 0.01606004 ;
Number of iterations: 13 ;
Converged: TRUE ;
Time: 34.966 Seconds;
Normalized w: 0 - 1 ; 1 - 0.04408 ; 2 - 1.12336 ; 3 - 0.1743 ; 4 - 0.50575 ; 5 - 0.32675 ; 6 - 0 ; 7 - 0.39643 ; 8 - 0 ; 9 - 0.15396 ; 10 - 0 ;

Data Set 56 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 35 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1137 ;
pihat0 by ASH: 0.04829662 ;
Number of iterations: 19 ;
Converged: TRUE ;
Time: 49.545 Seconds;
Normalized w: 0 - 1 ; 1 - 0.0242 ; 2 - 0.6626 ; 3 - 0.14568 ; 4 - 1e-05 ; 5 - 0.18875 ; 6 - -1e-05 ; 7 - -0.08641 ; 8 - 0 ; 9 - -0.18926 ; 10 - 0 ;

Data Set 840 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 28 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1653 ;
pihat0 by ASH: 0.02316832 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 32.668 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03386 ; 2 - 1.06371 ; 3 - 0.02061 ; 4 - 0.47735 ; 5 - -0.17761 ; 6 - 0 ; 7 - -0.18251 ; 8 - 0 ; 9 - 0.00494 ; 10 - 0 ;

Data Set 858 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 16 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1506 ;
pihat0 by ASH: 0.05110069 ;
Number of iterations: 24 ;
Converged: TRUE ;
Time: 64.818 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02631 ; 2 - 0.74324 ; 3 - 0.00012 ; 4 - 0 ; 5 - 0.18718 ; 6 - 0 ; 7 - 0.26895 ; 8 - 0 ; 9 - 0.26988 ; 10 - 0 ;

Data Set 771 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 12 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 795 ;
pihat0 by ASH: 0.04316169 ;
Number of iterations: 24 ;
Converged: TRUE ;
Time: 63.272 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03535 ; 2 - 0.60192 ; 3 - 0.16687 ; 4 - 1e-05 ; 5 - 0.32794 ; 6 - -1e-05 ; 7 - 0.24166 ; 8 - 0 ; 9 - 0.13785 ; 10 - 0 ;

Data Set 389 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 11 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1028 ;
pihat0 by ASH: 0.03156173 ;
Number of iterations: 23 ;
Converged: TRUE ;
Time: 58.617 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01943 ; 2 - 0.62289 ; 3 - 0.12735 ; 4 - 0 ; 5 - -0.40981 ; 6 - 0 ; 7 - -0.78155 ; 8 - 0 ; 9 - -0.38953 ; 10 - 0 ;

Data Set 485 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 9 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 614 ;
pihat0 by ASH: 0.04794909 ;
Number of iterations: 24 ;
Converged: TRUE ;
Time: 60.645 Seconds;
Normalized w: 0 - 1 ; 1 - -0.0137 ; 2 - 0.54271 ; 3 - 0.06363 ; 4 - 1e-05 ; 5 - -0.10023 ; 6 - -1e-05 ; 7 - -0.35619 ; 8 - 0 ; 9 - -0.14194 ; 10 - 0 ;

Data Set 77 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 7 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1307 ;
pihat0 by ASH: 0.05151585 ;
Number of iterations: 33 ;
Converged: TRUE ;
Time: 85.686 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03063 ; 2 - 0.67045 ; 3 - 0.38972 ; 4 - 1e-05 ; 5 - -0.17946 ; 6 - -1e-05 ; 7 - -0.91648 ; 8 - 0 ; 9 - -0.60815 ; 10 - 0 ;

Data Set 984 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 7 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 689 ;
pihat0 by ASH: 0.04567195 ;
Number of iterations: 36 ;
Converged: TRUE ;
Time: 94.533 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01891 ; 2 - 0.69992 ; 3 - 0.15925 ; 4 - 0.17339 ; 5 - 0.26948 ; 6 - -5e-05 ; 7 - 0.24941 ; 8 - 0 ; 9 - 0.04416 ; 10 - 0 ;

Data Set 360 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 6 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1392 ;
pihat0 by ASH: 0.0308234 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 39.811 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03963 ; 2 - 1.04077 ; 3 - 0.11348 ; 4 - 0.40225 ; 5 - 0.05358 ; 6 - -1e-05 ; 7 - -0.1684 ; 8 - 0 ; 9 - -0.16217 ; 10 - 0 ;

Data Set 522 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 4 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1149 ;
pihat0 by ASH: 0.02083846 ;
Number of iterations: 22 ;
Converged: TRUE ;
Time: 54.492 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00803 ; 2 - 0.91639 ; 3 - -0.0064 ; 4 - 0.21282 ; 5 - -0.00408 ; 6 - -0.07281 ; 7 - 0.09212 ; 8 - 0 ; 9 - 0.04651 ; 10 - 0 ;

Data Set 22 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 508 ;
pihat0 by ASH: 0.03271534 ;
Number of iterations: 17 ;
Converged: TRUE ;
Time: 45.089 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00676 ; 2 - 0.5612 ; 3 - 0.05325 ; 4 - 0 ; 5 - -0.15278 ; 6 - 0 ; 7 - -0.32578 ; 8 - 0 ; 9 - -0.20008 ; 10 - 0 ;

Data Set 269 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 662 ;
pihat0 by ASH: 0.02787007 ;
Number of iterations: 16 ;
Converged: TRUE ;
Time: 42.631 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03306 ; 2 - 0.63365 ; 3 - -0.12595 ; 4 - 0 ; 5 - -0.13951 ; 6 - 0 ; 7 - -0.20819 ; 8 - 0 ; 9 - -0.21345 ; 10 - 0 ;

Data Set 403 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 227 ;
pihat0 by ASH: 0.0531628 ;
Number of iterations: 16 ;
Converged: TRUE ;
Time: 42.363 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00588 ; 2 - 0.64463 ; 3 - -0.03689 ; 4 - 5e-05 ; 5 - -0.08136 ; 6 - -0.07883 ; 7 - -0.20657 ; 8 - 0 ; 9 - -0.14869 ; 10 - 0 ;

Data Set 923 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1340 ;
pihat0 by ASH: 0.03239883 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 38.895 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02157 ; 2 - 0.9554 ; 3 - 0.15328 ; 4 - 0.33303 ; 5 - 0.29494 ; 6 - -1e-05 ; 7 - 0.19884 ; 8 - 0 ; 9 - 0.09103 ; 10 - 0 ;

Data Set 3 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 193 ;
pihat0 by ASH: 0.0465218 ;
Number of iterations: 24 ;
Converged: TRUE ;
Time: 64.396 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01518 ; 2 - 0.51743 ; 3 - 0.13297 ; 4 - 1e-05 ; 5 - -0.08609 ; 6 - -1e-05 ; 7 - -0.27966 ; 8 - 0 ; 9 - -0.1633 ; 10 - 0 ;

Medium effects \(g_m\)

g = g.m.n

Data Set 355 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 639 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 2300 ;
pihat0 by ASH: 0.04750946 ;
Number of iterations: 19 ;
Converged: TRUE ;
Time: 52.569 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00306 ; 2 - 0.92729 ; 3 - -0.10268 ; 4 - 1e-05 ; 5 - -0.8234 ; 6 - 0 ; 7 - -1.36406 ; 8 - 0 ; 9 - -0.64319 ; 10 - 0 ;

Data Set 23 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 408 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 2448 ;
pihat0 by ASH: 0.03139009 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 33.494 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02055 ; 2 - 1.20582 ; 3 - 0.10727 ; 4 - 0.5808 ; 5 - 0.23667 ; 6 - -1e-05 ; 7 - 0.11689 ; 8 - 0 ; 9 - -0.03379 ; 10 - 0 ;

Data Set 122 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 331 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1822 ;
pihat0 by ASH: 0.04301549 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 50.354 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00013 ; 2 - 0.70701 ; 3 - -0.32429 ; 4 - 0 ; 5 - 0.02667 ; 6 - 0 ; 7 - 0.21896 ; 8 - 0 ; 9 - -0.0211 ; 10 - 0 ;

Data Set 749 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 114 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1685 ;
pihat0 by ASH: 0.02583276 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 48.827 Seconds;
Normalized w: 0 - 1 ; 1 - 0.0294 ; 2 - 0.82107 ; 3 - -0.04936 ; 4 - 1e-05 ; 5 - 0.02252 ; 6 - -1e-05 ; 7 - 0.39258 ; 8 - 0 ; 9 - 0.22657 ; 10 - 0 ;

Data Set 724 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 79 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1814 ;
pihat0 by ASH: 0.01606004 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 45.12 Seconds;
Normalized w: 0 - 1 ; 1 - 0.04424 ; 2 - 1.06414 ; 3 - 0.18173 ; 4 - 0.39882 ; 5 - 0.35799 ; 6 - -3e-05 ; 7 - 0.39599 ; 8 - 0 ; 9 - 0.22084 ; 10 - 0 ;

Data Set 56 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 35 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1137 ;
pihat0 by ASH: 0.04829662 ;
Number of iterations: 20 ;
Converged: TRUE ;
Time: 54.702 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00082 ; 2 - 0.6026 ; 3 - -0.06607 ; 4 - 1e-05 ; 5 - -0.47645 ; 6 - -1e-05 ; 7 - -0.77571 ; 8 - 0 ; 9 - -0.45166 ; 10 - 0 ;

Data Set 840 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 28 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1653 ;
pihat0 by ASH: 0.02316832 ;
Number of iterations: 14 ;
Converged: TRUE ;
Time: 39.137 Seconds;
Normalized w: 0 - 1 ; 1 - -0.04406 ; 2 - 1.03543 ; 3 - 0.03777 ; 4 - 0.4499 ; 5 - -0.09063 ; 6 - -3e-05 ; 7 - -0.15348 ; 8 - 0 ; 9 - -0.0621 ; 10 - 0 ;

Data Set 858 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 16 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1506 ;
pihat0 by ASH: 0.05110069 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 41.139 Seconds;
Normalized w: 0 - 1 ; 1 - -0.0213 ; 2 - 0.78002 ; 3 - 0.09871 ; 4 - 1e-05 ; 5 - 0.51491 ; 6 - -1e-05 ; 7 - 0.86345 ; 8 - 0 ; 9 - 0.48986 ; 10 - 0 ;

Data Set 771 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 12 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 795 ;
pihat0 by ASH: 0.04316169 ;
Number of iterations: 19 ;
Converged: TRUE ;
Time: 51.078 Seconds;
Normalized w: 0 - 1 ; 1 - -0.0218 ; 2 - 0.57477 ; 3 - 0.06145 ; 4 - 1e-05 ; 5 - -0.07979 ; 6 - -1e-05 ; 7 - -0.56023 ; 8 - 0 ; 9 - -0.35679 ; 10 - 0 ;

Data Set 389 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 11 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1028 ;
pihat0 by ASH: 0.03156173 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 58.432 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01264 ; 2 - 0.61679 ; 3 - 0.28078 ; 4 - 1e-05 ; 5 - 0.3165 ; 6 - -1e-05 ; 7 - 0.35502 ; 8 - 0 ; 9 - 0.32836 ; 10 - 0 ;

Data Set 485 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 9 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 614 ;
pihat0 by ASH: 0.04794909 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 53.04 Seconds;
Normalized w: 0 - 1 ; 1 - -0.0275 ; 2 - 0.54894 ; 3 - 0.12829 ; 4 - 2e-05 ; 5 - 0.11347 ; 6 - -2e-05 ; 7 - -0.16311 ; 8 - 0 ; 9 - -0.1432 ; 10 - 0 ;

Data Set 77 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 7 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1307 ;
pihat0 by ASH: 0.05151585 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 57.237 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00681 ; 2 - 0.65693 ; 3 - 0.159 ; 4 - 1e-05 ; 5 - -0.73516 ; 6 - -1e-05 ; 7 - -1.60706 ; 8 - 0 ; 9 - -0.82566 ; 10 - 0 ;

Data Set 984 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 7 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 689 ;
pihat0 by ASH: 0.04567195 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 58.335 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02396 ; 2 - 0.52771 ; 3 - 0.07993 ; 4 - 1e-05 ; 5 - 0.08646 ; 6 - -1e-05 ; 7 - 0.05192 ; 8 - 0 ; 9 - 0.06357 ; 10 - 0 ;

Data Set 360 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 6 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1392 ;
pihat0 by ASH: 0.0308234 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 41.466 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02125 ; 2 - 0.99264 ; 3 - 0.09947 ; 4 - 0.31108 ; 5 - 0.11964 ; 6 - -4e-05 ; 7 - -0.1291 ; 8 - 0 ; 9 - -0.15018 ; 10 - 0 ;

Data Set 522 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 4 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1149 ;
pihat0 by ASH: 0.02083846 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 32.783 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02656 ; 2 - 0.84155 ; 3 - -0.11024 ; 4 - 5e-05 ; 5 - -0.16279 ; 6 - -0.21037 ; 7 - -0.07362 ; 8 - 1e-05 ; 9 - -0.03288 ; 10 - 0 ;

Data Set 22 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 508 ;
pihat0 by ASH: 0.03271534 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 39.924 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03057 ; 2 - 0.56741 ; 3 - 0.11359 ; 4 - 0 ; 5 - 0.0741 ; 6 - 0 ; 7 - -0.01089 ; 8 - 0 ; 9 - 0.02849 ; 10 - 0 ;

Data Set 269 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 662 ;
pihat0 by ASH: 0.02787007 ;
Number of iterations: 22 ;
Converged: TRUE ;
Time: 60.898 Seconds;
Normalized w: 0 - 1 ; 1 - 0.04514 ; 2 - 0.61743 ; 3 - -0.13548 ; 4 - 1e-05 ; 5 - -0.07027 ; 6 - -1e-05 ; 7 - -0.26 ; 8 - 0 ; 9 - -0.33405 ; 10 - 0 ;

Data Set 403 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 227 ;
pihat0 by ASH: 0.0531628 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 32.91 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00172 ; 2 - 0.58524 ; 3 - 0.03575 ; 4 - 3e-05 ; 5 - 0.22562 ; 6 - -0.02133 ; 7 - 0.28009 ; 8 - 0 ; 9 - 0.13358 ; 10 - 0 ;

Data Set 923 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1340 ;
pihat0 by ASH: 0.03239883 ;
Number of iterations: 33 ;
Converged: TRUE ;
Time: 92.859 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00082 ; 2 - 0.78286 ; 3 - 0.0764 ; 4 - 0.01838 ; 5 - 0.04571 ; 6 - -0.10696 ; 7 - -0.12814 ; 8 - 0 ; 9 - -0.12938 ; 10 - 0 ;

Data Set 3 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 193 ;
pihat0 by ASH: 0.0465218 ;
Number of iterations: 14 ;
Converged: TRUE ;
Time: 39.657 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01078 ; 2 - 0.51478 ; 3 - 0.16499 ; 4 - 0 ; 5 - 0.00335 ; 6 - 0 ; 7 - -0.19617 ; 8 - 0 ; 9 - -0.11882 ; 10 - 0 ;

Large effects \(g_l\)

g = g.l.n

Data Set 355 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 639 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 2300 ;
pihat0 by ASH: 0.04750946 ;
Number of iterations: 24 ;
Converged: TRUE ;
Time: 66.244 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03817 ; 2 - 0.882 ; 3 - 0.14881 ; 4 - 1e-05 ; 5 - -0.23349 ; 6 - -1e-05 ; 7 - -0.5336 ; 8 - 0 ; 9 - -0.15809 ; 10 - 0 ;

Data Set 23 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 408 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 2448 ;
pihat0 by ASH: 0.03139009 ;
Number of iterations: 9 ;
Converged: TRUE ;
Time: 26.52 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03505 ; 2 - 1.26792 ; 3 - 0.16153 ; 4 - 0.62603 ; 5 - 0.22558 ; 6 - -2e-05 ; 7 - 0.09388 ; 8 - 0 ; 9 - 0.07425 ; 10 - 0 ;

Data Set 122 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 331 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1822 ;
pihat0 by ASH: 0.04301549 ;
Number of iterations: 30 ;
Converged: TRUE ;
Time: 87.749 Seconds;
Normalized w: 0 - 1 ; 1 - -0.0317 ; 2 - 0.94412 ; 3 - -0.46038 ; 4 - 0.3353 ; 5 - -0.59597 ; 6 - -2e-05 ; 7 - -0.32264 ; 8 - 0 ; 9 - -0.0767 ; 10 - 0 ;

Data Set 749 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 114 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1685 ;
pihat0 by ASH: 0.02583276 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 34.009 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02418 ; 2 - 0.88829 ; 3 - -0.0753 ; 4 - 0.23275 ; 5 - -0.13856 ; 6 - -6e-05 ; 7 - -0.00554 ; 8 - 0 ; 9 - 0.04905 ; 10 - 0 ;

Data Set 724 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 79 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1814 ;
pihat0 by ASH: 0.01606004 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 44.642 Seconds;
Normalized w: 0 - 1 ; 1 - 0.05007 ; 2 - 1.01824 ; 3 - 0.04034 ; 4 - 0.32956 ; 5 - -0.0786 ; 6 - -0.00011 ; 7 - -0.17934 ; 8 - 1e-05 ; 9 - -0.08416 ; 10 - 0 ;

Data Set 56 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 35 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1137 ;
pihat0 by ASH: 0.04829662 ;
Number of iterations: 33 ;
Converged: TRUE ;
Time: 97.409 Seconds;
Normalized w: 0 - 1 ; 1 - 0.05412 ; 2 - 0.58271 ; 3 - 0.31712 ; 4 - 3e-05 ; 5 - 0.61706 ; 6 - -2e-05 ; 7 - 0.74448 ; 8 - 0 ; 9 - 0.41563 ; 10 - 0 ;

Data Set 840 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 28 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1653 ;
pihat0 by ASH: 0.02316832 ;
Number of iterations: 9 ;
Converged: TRUE ;
Time: 26.425 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02649 ; 2 - 0.99776 ; 3 - 0.0356 ; 4 - 0.38774 ; 5 - -0.06081 ; 6 - -9e-05 ; 7 - 0.10143 ; 8 - 0 ; 9 - 0.22593 ; 10 - 0 ;

Data Set 858 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 16 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1506 ;
pihat0 by ASH: 0.05110069 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 51.258 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03991 ; 2 - 0.70312 ; 3 - -0.05927 ; 4 - 1e-05 ; 5 - -0.10238 ; 6 - -1e-05 ; 7 - -0.07577 ; 8 - 0 ; 9 - 0.00046 ; 10 - 0 ;

Data Set 771 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 12 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 795 ;
pihat0 by ASH: 0.04316169 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 42.649 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03928 ; 2 - 0.59491 ; 3 - 0.17109 ; 4 - 2e-05 ; 5 - 0.32763 ; 6 - -1e-05 ; 7 - 0.26641 ; 8 - 0 ; 9 - 0.17108 ; 10 - 0 ;

Data Set 389 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 11 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1028 ;
pihat0 by ASH: 0.03156173 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 51.946 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01803 ; 2 - 0.60676 ; 3 - 0.15551 ; 4 - 1e-05 ; 5 - -0.26375 ; 6 - -1e-05 ; 7 - -0.60591 ; 8 - 0 ; 9 - -0.26305 ; 10 - 0 ;

Data Set 485 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 9 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 614 ;
pihat0 by ASH: 0.04794909 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 50.366 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02076 ; 2 - 0.57247 ; 3 - 0.15823 ; 4 - 3e-05 ; 5 - 0.26273 ; 6 - -3e-05 ; 7 - -0.03591 ; 8 - 0 ; 9 - -0.08516 ; 10 - 0 ;

Data Set 77 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 7 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1307 ;
pihat0 by ASH: 0.05151585 ;
Number of iterations: 24 ;
Converged: TRUE ;
Time: 69.149 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00627 ; 2 - 0.67236 ; 3 - 0.11823 ; 4 - 2e-05 ; 5 - -0.73785 ; 6 - -1e-05 ; 7 - -1.57253 ; 8 - 0 ; 9 - -0.81204 ; 10 - 0 ;

Data Set 984 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 7 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 689 ;
pihat0 by ASH: 0.04567195 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 45.815 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02534 ; 2 - 0.5573 ; 3 - 0.12584 ; 4 - 1e-05 ; 5 - 0.14666 ; 6 - -1e-05 ; 7 - 0.05466 ; 8 - 0 ; 9 - -0.04527 ; 10 - 0 ;

Data Set 360 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 6 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1392 ;
pihat0 by ASH: 0.0308234 ;
Number of iterations: 16 ;
Converged: TRUE ;
Time: 46.025 Seconds;
Normalized w: 0 - 1 ; 1 - 0.07432 ; 2 - 0.95992 ; 3 - 0.34187 ; 4 - 0.23308 ; 5 - 0.51137 ; 6 - -0.04451 ; 7 - 0.23136 ; 8 - 1e-05 ; 9 - -0.02381 ; 10 - 0 ;

Data Set 522 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 4 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1149 ;
pihat0 by ASH: 0.02083846 ;
Number of iterations: 10 ;
Converged: TRUE ;
Time: 28.332 Seconds;
Normalized w: 0 - 1 ; 1 - -0.0252 ; 2 - 0.79605 ; 3 - -0.16873 ; 4 - 6e-05 ; 5 - -0.3815 ; 6 - -0.1706 ; 7 - -0.40957 ; 8 - 1e-05 ; 9 - -0.20061 ; 10 - 0 ;

Data Set 22 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 508 ;
pihat0 by ASH: 0.03271534 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 41.664 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02032 ; 2 - 0.55753 ; 3 - 0.01993 ; 4 - 1e-05 ; 5 - -0.29328 ; 6 - -1e-05 ; 7 - -0.6299 ; 8 - 0 ; 9 - -0.37058 ; 10 - 0 ;

Data Set 269 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 662 ;
pihat0 by ASH: 0.02787007 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 35.238 Seconds;
Normalized w: 0 - 1 ; 1 - 0.04334 ; 2 - 0.63944 ; 3 - -0.04031 ; 4 - 8e-05 ; 5 - 0.29723 ; 6 - -0.07026 ; 7 - 0.56157 ; 8 - 1e-05 ; 9 - 0.27277 ; 10 - 0 ;

Data Set 403 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 227 ;
pihat0 by ASH: 0.0531628 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 35.472 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01072 ; 2 - 0.60096 ; 3 - 0.06469 ; 4 - 2e-05 ; 5 - 0.16915 ; 6 - -0.00992 ; 7 - 0.13881 ; 8 - 1e-05 ; 9 - 0.01755 ; 10 - 0 ;

Data Set 923 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 1340 ;
pihat0 by ASH: 0.03239883 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 41.377 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01909 ; 2 - 0.93685 ; 3 - -0.07433 ; 4 - 0.27769 ; 5 - -0.30218 ; 6 - -0.00012 ; 7 - -0.39988 ; 8 - 1e-05 ; 9 - -0.17585 ; 10 - 0 ;

Data Set 3 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 193 ;
pihat0 by ASH: 0.0465218 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 34.66 Seconds;
Normalized w: 0 - 1 ; 1 - 0.0369 ; 2 - 0.52344 ; 3 - 0.16537 ; 4 - 0 ; 5 - -0.13339 ; 6 - 0 ; 7 - -0.44877 ; 8 - 0 ; 9 - -0.23269 ; 10 - 0 ;

Category III: Friendly

label = "friendly"

Global null \(g_n\)

g = g.null

Data Set 4 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.935 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 5 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.786 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 7 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.19 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 8 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.452 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 9 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.907 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 12 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.756 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 13 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.3 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 14 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.462 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 16 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.799 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 17 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 5000 ;
Converged: FALSE ;
Time: 12642.71 Seconds;
Normalized w: 0 - 1 ; 1 - -1.33446 ; 2 - -1.8488 ; 3 - -7.56469 ; 4 - -4.30848 ; 5 - -17.12818 ; 6 - -4.49198 ; 7 - -18.13845 ; 8 - 0 ; 9 - -7.44202 ; 10 - 1.8392 ;

Data Set 18 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 3.958 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 25 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 3 ;
Converged: TRUE ;
Time: 5.831 Seconds;
Normalized w: 0 - 1 ; 1 - -0.06372 ; 2 - -0.37063 ; 3 - -0.28824 ; 4 - 0 ; 5 - -0.7425 ; 6 - -0.26211 ; 7 - -0.80769 ; 8 - -0.03205 ; 9 - -0.40298 ; 10 - 0 ;

Data Set 28 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.585 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 30 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.698 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 34 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 3 ;
Converged: TRUE ;
Time: 6.65 Seconds;
Normalized w: 0 - 1 ; 1 - 10.27198 ; 2 - -10.18684 ; 3 - 50.28912 ; 4 - -25.22942 ; 5 - 99.4042 ; 6 - -22.33555 ; 7 - 90.85975 ; 8 - 0 ; 9 - 31.91951 ; 10 - 6.40972 ;

Data Set 35 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.301 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 36 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 37.366 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00964 ; 2 - -0.20509 ; 3 - -0.02656 ; 4 - 0.05762 ; 5 - -0.00135 ; 6 - -6e-05 ; 7 - -0.02009 ; 8 - 0 ; 9 - -0.01223 ; 10 - 0 ;

Data Set 38 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.454 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 42 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.712 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 43 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.323 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 45 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.308 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 46 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.535 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 47 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.261 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 49 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.245 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 52 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 3.879 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 53 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 3.897 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set 54 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.985 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Small effects \(g_s\)

g = g.s.n

Data Set 4 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 32 ;
Converged: TRUE ;
Time: 64.773 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02636 ; 2 - 9e-05 ; 3 - 0.00083 ; 4 - -0.11699 ; 5 - -0.06146 ; 6 - 4e-05 ; 7 - -0.00813 ; 8 - 0 ; 9 - -0.00432 ; 10 - 0 ;

Data Set 5 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 24.007 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00566 ; 2 - -0.012 ; 3 - -0.01422 ; 4 - 0 ; 5 - 0.01039 ; 6 - 0 ; 7 - 0.02004 ; 8 - 0 ; 9 - 0.00684 ; 10 - 0 ;

Data Set 7 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 16 ;
Converged: TRUE ;
Time: 34.91 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00477 ; 2 - -1e-04 ; 3 - -0.04082 ; 4 - 0 ; 5 - -0.02149 ; 6 - 1e-05 ; 7 - -0.0494 ; 8 - 0 ; 9 - 0.04647 ; 10 - 0 ;

Data Set 8 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 33.1 Seconds;
Normalized w: 0 - 1 ; 1 - 0.04715 ; 2 - -0.05058 ; 3 - -0.05803 ; 4 - 0.17916 ; 5 - -0.11077 ; 6 - -2e-05 ; 7 - -0.19 ; 8 - 0 ; 9 - -0.05073 ; 10 - 0 ;

Data Set 9 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 33.273 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02096 ; 2 - 0.19152 ; 3 - -0.03815 ; 4 - 0 ; 5 - 0.01881 ; 6 - 0 ; 7 - 0.01714 ; 8 - 0 ; 9 - 0.01057 ; 10 - 0 ;

Data Set 12 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 17 ;
Converged: TRUE ;
Time: 37.544 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01447 ; 2 - -1e-05 ; 3 - -0.0028 ; 4 - 0.04127 ; 5 - 0.16758 ; 6 - -1e-05 ; 7 - 0.1316 ; 8 - 0 ; 9 - 0.07944 ; 10 - 0 ;

Data Set 13 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 44.306 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02194 ; 2 - 0.00749 ; 3 - 0.03846 ; 4 - -0.03403 ; 5 - 0.09693 ; 6 - 0 ; 7 - -0.01576 ; 8 - 0 ; 9 - -0.02506 ; 10 - 0 ;

Data Set 14 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 42.428 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01485 ; 2 - -7e-05 ; 3 - 0.02494 ; 4 - 0.0162 ; 5 - -0.03506 ; 6 - -1e-05 ; 7 - -0.01308 ; 8 - 0 ; 9 - -0.01309 ; 10 - 0 ;

Data Set 16 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 35 ;
Converged: TRUE ;
Time: 73.559 Seconds;
Normalized w: 0 - 1 ; 1 - 0.0157 ; 2 - -0.01385 ; 3 - 0.01775 ; 4 - 0.04667 ; 5 - -0.03378 ; 6 - 0 ; 7 - -0.06943 ; 8 - 0 ; 9 - -0.06172 ; 10 - 0 ;

Data Set 17 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 27 ;
Converged: TRUE ;
Time: 59.747 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01246 ; 2 - -0.14903 ; 3 - -0.05703 ; 4 - 0 ; 5 - -0.05395 ; 6 - 1e-05 ; 7 - -0.11485 ; 8 - -1e-05 ; 9 - -0.01845 ; 10 - 0 ;

Data Set 18 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 14 ;
Converged: TRUE ;
Time: 30.253 Seconds;
Normalized w: 0 - 1 ; 1 - -0.06071 ; 2 - -0.02478 ; 3 - -0.01881 ; 4 - 0 ; 5 - -0.03655 ; 6 - 1e-05 ; 7 - 0.03296 ; 8 - 0 ; 9 - 0.02574 ; 10 - 0 ;

Data Set 25 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 26.651 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01302 ; 2 - -0.0295 ; 3 - -0.02165 ; 4 - 0.20784 ; 5 - -0.02653 ; 6 - 0 ; 7 - 0.00136 ; 8 - 0 ; 9 - -0.01427 ; 10 - 0 ;

Data Set 28 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 5001 ;
Converged: FALSE ;
Time: 10302.82 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01216 ; 2 - 0.1115 ; 3 - -0.01235 ; 4 - 0 ; 5 - 0.07868 ; 6 - 0 ; 7 - 0.11383 ; 8 - 0 ; 9 - 0.12545 ; 10 - 0 ;

Data Set 30 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 22 ;
Converged: TRUE ;
Time: 43.887 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01363 ; 2 - 0.05651 ; 3 - 0.00107 ; 4 - -2e-05 ; 5 - 0.11668 ; 6 - 0.06284 ; 7 - 0.15866 ; 8 - -1e-05 ; 9 - 0.15361 ; 10 - 0 ;

Data Set 34 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 27 ;
Converged: TRUE ;
Time: 61.299 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00632 ; 2 - -0.01831 ; 3 - 0.13477 ; 4 - 2e-05 ; 5 - 0.12953 ; 6 - 0 ; 7 - 0.1476 ; 8 - 0 ; 9 - 0.04906 ; 10 - 0 ;

Data Set 35 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 32 ;
Converged: TRUE ;
Time: 69.24 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02322 ; 2 - -0.161 ; 3 - -0.07007 ; 4 - 0.05178 ; 5 - 0.02032 ; 6 - 0 ; 7 - 0.04373 ; 8 - 0 ; 9 - 0.09596 ; 10 - 0 ;

Data Set 36 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 28 ;
Converged: TRUE ;
Time: 60.044 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02316 ; 2 - -0.02323 ; 3 - 0.01329 ; 4 - 0.0851 ; 5 - 0.09681 ; 6 - 0 ; 7 - 0.11939 ; 8 - 0 ; 9 - 0.06562 ; 10 - 0 ;

Data Set 38 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 31 ;
Converged: TRUE ;
Time: 59.455 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00126 ; 2 - -9e-05 ; 3 - 0.03421 ; 4 - 0.11448 ; 5 - 0.08018 ; 6 - 0 ; 7 - 0.06515 ; 8 - 0 ; 9 - 0.01129 ; 10 - 0 ;

Data Set 42 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 17 ;
Converged: TRUE ;
Time: 36.075 Seconds;
Normalized w: 0 - 1 ; 1 - -0.05045 ; 2 - -0.03073 ; 3 - 0.00187 ; 4 - 0.17066 ; 5 - 0.043 ; 6 - -1e-05 ; 7 - 0.10546 ; 8 - 0 ; 9 - 0.06128 ; 10 - 0 ;

Data Set 43 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 28 ;
Converged: TRUE ;
Time: 57.174 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00436 ; 2 - -0.0157 ; 3 - 0.04563 ; 4 - 0.14063 ; 5 - 0.07373 ; 6 - -3e-05 ; 7 - 0.07293 ; 8 - 0 ; 9 - 0.04383 ; 10 - 0 ;

Data Set 45 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 32.734 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01758 ; 2 - -2e-05 ; 3 - -0.02237 ; 4 - 0.12239 ; 5 - -0.07787 ; 6 - 0 ; 7 - -0.02378 ; 8 - 0 ; 9 - 0.01755 ; 10 - 0 ;

Data Set 46 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 27 ;
Converged: TRUE ;
Time: 59.071 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01539 ; 2 - 0.00427 ; 3 - 0.008 ; 4 - -1e-05 ; 5 - -0.05233 ; 6 - 0 ; 7 - -0.00013 ; 8 - 0 ; 9 - -0.01379 ; 10 - 0 ;

Data Set 47 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 34.069 Seconds;
Normalized w: 0 - 1 ; 1 - 0.06924 ; 2 - -1e-05 ; 3 - 0.01834 ; 4 - 0.11038 ; 5 - 0.1185 ; 6 - -2e-05 ; 7 - 0.12858 ; 8 - 0 ; 9 - 0.07942 ; 10 - 0 ;

Data Set 49 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 86 ;
Converged: TRUE ;
Time: 183.336 Seconds;
Normalized w: 0 - 1 ; 1 - -0.07177 ; 2 - -0.00033 ; 3 - 0.00816 ; 4 - 0.04115 ; 5 - -0.09252 ; 6 - -1e-05 ; 7 - -0.12241 ; 8 - 0 ; 9 - -0.08512 ; 10 - 0 ;

Data Set 52 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 42.323 Seconds;
Normalized w: 0 - 1 ; 1 - 0.07525 ; 2 - 0.14479 ; 3 - 0.04206 ; 4 - -7e-05 ; 5 - 0.07778 ; 6 - 1e-05 ; 7 - 0.13161 ; 8 - 0 ; 9 - 0.01941 ; 10 - 0 ;

Data Set 53 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 5001 ;
Converged: FALSE ;
Time: 10074.4 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00993 ; 2 - 0.0382 ; 3 - -0.03964 ; 4 - -0.07542 ; 5 - -0.07327 ; 6 - 0 ; 7 - -0.02457 ; 8 - 0 ; 9 - -0.01905 ; 10 - 0 ;

Data Set 54 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 40.702 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01673 ; 2 - -1e-05 ; 3 - -0.01073 ; 4 - 0.06691 ; 5 - -0.13847 ; 6 - 0 ; 7 - -0.26718 ; 8 - 0 ; 9 - -0.17156 ; 10 - 0 ;

Medium effects \(g_m\)

g = g.m.n

Data Set 4 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 26.82 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03267 ; 2 - 6e-05 ; 3 - 0.01728 ; 4 - -0.05125 ; 5 - -0.01797 ; 6 - 6e-05 ; 7 - 0.02455 ; 8 - 0 ; 9 - 0.02645 ; 10 - 0 ;

Data Set 5 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 33.054 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00261 ; 2 - -0.02329 ; 3 - -0.0222 ; 4 - 0 ; 5 - -0.1049 ; 6 - 1e-05 ; 7 - -0.19139 ; 8 - 0 ; 9 - -0.14833 ; 10 - 0 ;

Data Set 7 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 33.715 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00828 ; 2 - -0.09333 ; 3 - -0.00674 ; 4 - 3e-05 ; 5 - 0.06208 ; 6 - 0 ; 7 - -0.00506 ; 8 - 0 ; 9 - 0.02727 ; 10 - 0 ;

Data Set 8 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 40.271 Seconds;
Normalized w: 0 - 1 ; 1 - 0.07919 ; 2 - -0.0795 ; 3 - 0.03356 ; 4 - 0.2086 ; 5 - 0.16389 ; 6 - -2e-05 ; 7 - 0.1661 ; 8 - 0 ; 9 - 0.07984 ; 10 - 0 ;

Data Set 9 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 24 ;
Converged: TRUE ;
Time: 52.506 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02944 ; 2 - 0.00154 ; 3 - 0.0485 ; 4 - -0.14479 ; 5 - 0.22889 ; 6 - 3e-05 ; 7 - 0.23946 ; 8 - 0 ; 9 - 0.12409 ; 10 - 0 ;

Data Set 12 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 47.494 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03432 ; 2 - -1e-04 ; 3 - -0.02624 ; 4 - 0.05091 ; 5 - 0.15142 ; 6 - -1e-05 ; 7 - 0.15588 ; 8 - 0 ; 9 - 0.14077 ; 10 - 0 ;

Data Set 13 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 13 ;
Converged: TRUE ;
Time: 29.48 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01267 ; 2 - 6e-05 ; 3 - -0.13406 ; 4 - -3e-05 ; 5 - -0.1933 ; 6 - 1e-05 ; 7 - -0.30924 ; 8 - 0 ; 9 - -0.14825 ; 10 - 0 ;

Data Set 14 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 40.641 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02507 ; 2 - -0.06364 ; 3 - 0.10035 ; 4 - 2e-05 ; 5 - 0.18953 ; 6 - 0 ; 7 - 0.20852 ; 8 - 0 ; 9 - 0.08675 ; 10 - 0 ;

Data Set 16 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 26 ;
Converged: TRUE ;
Time: 56.766 Seconds;
Normalized w: 0 - 1 ; 1 - 0.0187 ; 2 - -0.06206 ; 3 - 0.09323 ; 4 - 0.0618 ; 5 - 0.1623 ; 6 - 0 ; 7 - 0.18365 ; 8 - 0 ; 9 - 0.0706 ; 10 - 0 ;

Data Set 17 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 5001 ;
Converged: FALSE ;
Time: 11100.76 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03447 ; 2 - -0.05523 ; 3 - 0.06195 ; 4 - 0.11262 ; 5 - 0.08817 ; 6 - 0 ; 7 - 0.03342 ; 8 - 0 ; 9 - 0.00959 ; 10 - 0 ;

Data Set 18 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 33.869 Seconds;
Normalized w: 0 - 1 ; 1 - -0.0541 ; 2 - -0.0507 ; 3 - 0.00158 ; 4 - -1e-05 ; 5 - -0.0265 ; 6 - 2e-04 ; 7 - 0.04921 ; 8 - -1e-05 ; 9 - 0.02677 ; 10 - 0 ;

Data Set 25 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 40.277 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02588 ; 2 - -4e-04 ; 3 - -0.08092 ; 4 - 0.32666 ; 5 - -0.23836 ; 6 - -1e-05 ; 7 - -0.31599 ; 8 - 0 ; 9 - -0.23587 ; 10 - 0 ;

Data Set 28 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 45.188 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01256 ; 2 - 0.0546 ; 3 - -0.01844 ; 4 - -0.0286 ; 5 - 0.04602 ; 6 - 0 ; 7 - 0.07252 ; 8 - 0 ; 9 - 0.13857 ; 10 - 0 ;

Data Set 30 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 13 ;
Converged: TRUE ;
Time: 29.311 Seconds;
Normalized w: 0 - 1 ; 1 - -0.0106 ; 2 - 1e-05 ; 3 - 0.01086 ; 4 - -2e-05 ; 5 - 0.05755 ; 6 - 0.08278 ; 7 - -0.16644 ; 8 - -1e-05 ; 9 - -0.09262 ; 10 - 0 ;

Data Set 34 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 46.701 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03556 ; 2 - -0.05027 ; 3 - 0.00709 ; 4 - 0.01514 ; 5 - -0.31879 ; 6 - 0 ; 7 - -0.39227 ; 8 - 0 ; 9 - -0.16133 ; 10 - 0 ;

Data Set 35 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 33 ;
Converged: TRUE ;
Time: 69.863 Seconds;
Normalized w: 0 - 1 ; 1 - 0.04229 ; 2 - -0.23491 ; 3 - -0.05601 ; 4 - 0.06879 ; 5 - -0.00842 ; 6 - 0 ; 7 - -0.10959 ; 8 - 0 ; 9 - 0.01238 ; 10 - 0 ;

Data Set 36 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 30 ;
Converged: TRUE ;
Time: 59.411 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00538 ; 2 - -0.21941 ; 3 - -0.0037 ; 4 - 0.05565 ; 5 - 0.09608 ; 6 - 0 ; 7 - 0.19913 ; 8 - 0 ; 9 - 0.17585 ; 10 - 0 ;

Data Set 38 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 19 ;
Converged: TRUE ;
Time: 42.036 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01094 ; 2 - -0.02397 ; 3 - -0.12459 ; 4 - 0.17387 ; 5 - -0.31723 ; 6 - 0 ; 7 - -0.45859 ; 8 - 0 ; 9 - -0.25436 ; 10 - 0 ;

Data Set 42 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 39.952 Seconds;
Normalized w: 0 - 1 ; 1 - -0.0482 ; 2 - -0.01389 ; 3 - -0.065 ; 4 - 0.27854 ; 5 - -0.09584 ; 6 - -1e-05 ; 7 - 0.0142 ; 8 - 0 ; 9 - 0.08629 ; 10 - 0 ;

Data Set 43 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 22 ;
Converged: TRUE ;
Time: 46.905 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03433 ; 2 - -0.19453 ; 3 - -0.10223 ; 4 - 0.12601 ; 5 - -0.20707 ; 6 - -1e-05 ; 7 - -0.1028 ; 8 - 0 ; 9 - -0.0216 ; 10 - 0 ;

Data Set 45 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 25 ;
Converged: TRUE ;
Time: 50.949 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03197 ; 2 - -0.08215 ; 3 - 0.09968 ; 4 - 0.10778 ; 5 - 0.13692 ; 6 - -1e-05 ; 7 - 0.1704 ; 8 - 0 ; 9 - 0.11482 ; 10 - 0 ;

Data Set 46 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 10 ;
Converged: TRUE ;
Time: 21.11 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00434 ; 2 - 1e-05 ; 3 - 0.14845 ; 4 - -0.01023 ; 5 - 0.27126 ; 6 - 4e-05 ; 7 - 0.35912 ; 8 - 0 ; 9 - 0.13341 ; 10 - 0 ;

Data Set 47 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 33.65 Seconds;
Normalized w: 0 - 1 ; 1 - 0.04624 ; 2 - -6e-05 ; 3 - -0.03236 ; 4 - 0.14292 ; 5 - 0.08857 ; 6 - -1e-05 ; 7 - 0.0338 ; 8 - 0 ; 9 - 0.00538 ; 10 - 0 ;

Data Set 49 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 47.63 Seconds;
Normalized w: 0 - 1 ; 1 - -0.07053 ; 2 - -0.0848 ; 3 - 0.07752 ; 4 - 1e-05 ; 5 - 0.10336 ; 6 - 0 ; 7 - 0.17414 ; 8 - 0 ; 9 - 0.0728 ; 10 - 0 ;

Data Set 52 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 16 ;
Converged: TRUE ;
Time: 35.713 Seconds;
Normalized w: 0 - 1 ; 1 - 0.05611 ; 2 - 2e-05 ; 3 - -0.108 ; 4 - -0.06902 ; 5 - -0.31934 ; 6 - 8e-05 ; 7 - -0.36428 ; 8 - 0 ; 9 - -0.2361 ; 10 - 0 ;

Data Set 53 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 33.108 Seconds;
Normalized w: 0 - 1 ; 1 - -0.023 ; 2 - 0.00015 ; 3 - 0.00543 ; 4 - -0.02917 ; 5 - 0.01581 ; 6 - 2e-05 ; 7 - 0.11833 ; 8 - 0 ; 9 - 0.09681 ; 10 - 0 ;

Data Set 54 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 36 ;
Converged: TRUE ;
Time: 78.558 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01614 ; 2 - -0.12656 ; 3 - -0.16532 ; 4 - 0.03757 ; 5 - -0.39897 ; 6 - 0 ; 7 - -0.50568 ; 8 - 0 ; 9 - -0.2648 ; 10 - 0 ;

Large effects \(g_l\)

g = g.l.n

Data Set 4 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 27.268 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00045 ; 2 - 0 ; 3 - 0.0088 ; 4 - -0.02504 ; 5 - -0.26885 ; 6 - 0.00465 ; 7 - -0.38568 ; 8 - -1e-05 ; 9 - -0.22969 ; 10 - 0 ;

Data Set 5 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 34.1 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00415 ; 2 - -0.15722 ; 3 - -0.11379 ; 4 - -5e-05 ; 5 - -0.42688 ; 6 - 0.0123 ; 7 - -0.61534 ; 8 - -1e-05 ; 9 - -0.36652 ; 10 - 0 ;

Data Set 7 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 34.194 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00843 ; 2 - -0.14834 ; 3 - -0.16054 ; 4 - 3e-05 ; 5 - -0.22841 ; 6 - 0 ; 7 - -0.3338 ; 8 - 0 ; 9 - -0.14564 ; 10 - 0 ;

Data Set 8 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 47.519 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02756 ; 2 - -0.1365 ; 3 - -0.15919 ; 4 - 0.24379 ; 5 - -0.16529 ; 6 - -2e-05 ; 7 - -0.22038 ; 8 - 0 ; 9 - -0.09857 ; 10 - 0 ;

Data Set 9 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 43.273 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02243 ; 2 - -3e-05 ; 3 - -0.04545 ; 4 - -0.14285 ; 5 - 0.09466 ; 6 - 0.00572 ; 7 - 0.18346 ; 8 - -1e-05 ; 9 - 0.12654 ; 10 - 0 ;

Data Set 12 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 34.367 Seconds;
Normalized w: 0 - 1 ; 1 - -0.05692 ; 2 - -0.11116 ; 3 - -0.08914 ; 4 - 0.00011 ; 5 - -0.06715 ; 6 - -1e-05 ; 7 - -0.11975 ; 8 - 0 ; 9 - -0.02595 ; 10 - 0 ;

Data Set 13 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 40.186 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02001 ; 2 - -0.02833 ; 3 - -0.12276 ; 4 - -0.01949 ; 5 - -0.06265 ; 6 - 0.00023 ; 7 - -0.00407 ; 8 - -1e-05 ; 9 - 0.03647 ; 10 - 0 ;

Data Set 14 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 34.924 Seconds;
Normalized w: 0 - 1 ; 1 - -0.04048 ; 2 - -0.1153 ; 3 - -0.07993 ; 4 - 2e-05 ; 5 - -0.18083 ; 6 - 0 ; 7 - -0.22016 ; 8 - 0 ; 9 - -0.12694 ; 10 - 0 ;

Data Set 16 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 27 ;
Converged: TRUE ;
Time: 58.692 Seconds;
Normalized w: 0 - 1 ; 1 - 0.0293 ; 2 - -0.18464 ; 3 - 0.10176 ; 4 - 5e-04 ; 5 - 0.0903 ; 6 - -1e-05 ; 7 - 0.04193 ; 8 - 0 ; 9 - -0.05872 ; 10 - 0 ;

Data Set 17 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 5002 ;
Converged: FALSE ;
Time: 11079.89 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01072 ; 2 - -0.26997 ; 3 - -0.07669 ; 4 - 6e-05 ; 5 - -0.04079 ; 6 - 0 ; 7 - 0.03529 ; 8 - 0 ; 9 - 0.09348 ; 10 - 0 ;

Data Set 18 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 35.346 Seconds;
Normalized w: 0 - 1 ; 1 - -0.04628 ; 2 - -0.11631 ; 3 - -0.09179 ; 4 - -2e-05 ; 5 - -0.34225 ; 6 - 0.00313 ; 7 - -0.37973 ; 8 - -2e-05 ; 9 - -0.18554 ; 10 - 0 ;

Data Set 25 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 28.082 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02622 ; 2 - -0.03915 ; 3 - -0.02422 ; 4 - 0.34895 ; 5 - -0.01946 ; 6 - -5e-04 ; 7 - 0.08685 ; 8 - 1e-05 ; 9 - 0.00936 ; 10 - 0 ;

Data Set 28 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 34.066 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01323 ; 2 - 0.00108 ; 3 - 0.00202 ; 4 - -0.00027 ; 5 - 0.17488 ; 6 - 1e-05 ; 7 - 0.15148 ; 8 - 0 ; 9 - 0.14806 ; 10 - 0 ;

Data Set 30 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 40.694 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03087 ; 2 - -0.08459 ; 3 - -0.09512 ; 4 - -4e-05 ; 5 - -0.10473 ; 6 - 0.10879 ; 7 - -0.14771 ; 8 - -1e-05 ; 9 - 0.01404 ; 10 - 0 ;

Data Set 34 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 34.761 Seconds;
Normalized w: 0 - 1 ; 1 - -0.04399 ; 2 - -0.16072 ; 3 - 0.00228 ; 4 - 2e-05 ; 5 - -0.08778 ; 6 - 0 ; 7 - 0.07589 ; 8 - 0 ; 9 - 0.12282 ; 10 - 0 ;

Data Set 35 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 48.306 Seconds;
Normalized w: 0 - 1 ; 1 - 0.0603 ; 2 - -0.26004 ; 3 - 0.06367 ; 4 - 0.06711 ; 5 - 0.3671 ; 6 - -1e-05 ; 7 - 0.4468 ; 8 - 0 ; 9 - 0.30513 ; 10 - 0 ;

Data Set 36 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 30 ;
Converged: TRUE ;
Time: 67.664 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03677 ; 2 - -0.2723 ; 3 - 0.0441 ; 4 - 0.00485 ; 5 - 0.06012 ; 6 - -1e-05 ; 7 - -0.01438 ; 8 - 0 ; 9 - -0.0428 ; 10 - 0 ;

Data Set 38 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 24 ;
Converged: TRUE ;
Time: 54.251 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00941 ; 2 - -0.28287 ; 3 - 0.00284 ; 4 - 0.05124 ; 5 - 0.01759 ; 6 - -2e-05 ; 7 - -0.02514 ; 8 - 0 ; 9 - -0.01087 ; 10 - 0 ;

Data Set 42 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 36.94 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03416 ; 2 - -0.15843 ; 3 - -0.01314 ; 4 - 0.23675 ; 5 - -0.20604 ; 6 - -1e-05 ; 7 - -0.36721 ; 8 - 0 ; 9 - -0.21288 ; 10 - 0 ;

Data Set 43 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 24 ;
Converged: TRUE ;
Time: 54.644 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00785 ; 2 - -0.26077 ; 3 - 0.1547 ; 4 - 0.10156 ; 5 - 0.36825 ; 6 - -1e-05 ; 7 - 0.63807 ; 8 - 0 ; 9 - 0.39089 ; 10 - 0 ;

Data Set 45 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 14 ;
Converged: TRUE ;
Time: 32.593 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01288 ; 2 - -0.1265 ; 3 - 0.04494 ; 4 - 0.16284 ; 5 - 0.22322 ; 6 - -1e-05 ; 7 - 0.30089 ; 8 - 0 ; 9 - 0.11998 ; 10 - 0 ;

Data Set 46 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 28.186 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01259 ; 2 - -0.02024 ; 3 - 0.06813 ; 4 - -3e-05 ; 5 - 0.13726 ; 6 - 5e-05 ; 7 - 0.24548 ; 8 - -1e-05 ; 9 - 0.13674 ; 10 - 0 ;

Data Set 47 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 23 ;
Converged: TRUE ;
Time: 51.481 Seconds;
Normalized w: 0 - 1 ; 1 - 0.03654 ; 2 - -0.084 ; 3 - -0.18685 ; 4 - 0.10076 ; 5 - -0.16623 ; 6 - -5e-05 ; 7 - -0.19907 ; 8 - 1e-05 ; 9 - -0.05351 ; 10 - 0 ;

Data Set 49 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 31.391 Seconds;
Normalized w: 0 - 1 ; 1 - -0.07447 ; 2 - -0.11275 ; 3 - 0.03258 ; 4 - -1e-05 ; 5 - -0.18303 ; 6 - 1e-05 ; 7 - -0.22966 ; 8 - 0 ; 9 - -0.11591 ; 10 - 0 ;

Data Set 52 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 26.992 Seconds;
Normalized w: 0 - 1 ; 1 - 0.09489 ; 2 - 6e-05 ; 3 - -0.05166 ; 4 - -0.09664 ; 5 - -0.30895 ; 6 - 3e-05 ; 7 - -0.4091 ; 8 - 0 ; 9 - -0.26597 ; 10 - 0 ;

Data Set 53 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 9 ;
Converged: TRUE ;
Time: 21.187 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01689 ; 2 - -1e-05 ; 3 - -0.01519 ; 4 - -0.00016 ; 5 - 0.04312 ; 6 - 0.00043 ; 7 - 0.15403 ; 8 - -1e-05 ; 9 - 0.1258 ; 10 - 0 ;

Data Set 54 ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 42.11 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01863 ; 2 - -0.25293 ; 3 - -0.07759 ; 4 - 0.00025 ; 5 - -0.25252 ; 6 - -1e-05 ; 7 - -0.26616 ; 8 - 0 ; 9 - -0.15442 ; 10 - 0 ;

Category III: iid

label = "iid"

Global null \(g_n\)

g = g.null

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9902233 ;
Number of iterations: 3 ;
Converged: TRUE ;
Time: 10.887 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01379 ; 2 - 0.00377 ; 3 - -0.03096 ; 4 - 0.00284 ; 5 - -0.08217 ; 6 - -0.00938 ; 7 - -0.13481 ; 8 - 0 ; 9 - -0.08577 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 10.502 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.442 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9980103 ;
Number of iterations: 8 ;
Converged: TRUE ;
Time: 18.522 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00183 ; 2 - -0.01608 ; 3 - 0.0013 ; 4 - -0.00013 ; 5 - 0.00274 ; 6 - 0.02018 ; 7 - -0.02614 ; 8 - 0 ; 9 - -0.0477 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9984696 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.827 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.737 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.583 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9978326 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 5.211 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 4.835 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 2 ;
Converged: TRUE ;
Time: 6.369 Seconds;
Normalized w: 0 - 1 ; 1 - 0 ; 2 - 0 ; 3 - 0 ; 4 - 0 ; 5 - 0 ; 6 - 0 ; 7 - 0 ; 8 - 0 ; 9 - 0 ; 10 - 0 ;

Small effects \(g_s\)

g = g.s.n

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9902233 ;
Number of iterations: 26 ;
Converged: TRUE ;
Time: 56.705 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01206 ; 2 - 1e-05 ; 3 - -0.0116 ; 4 - 1e-05 ; 5 - -0.11481 ; 6 - 0 ; 7 - -0.1881 ; 8 - 0 ; 9 - -0.08626 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 20 ;
Converged: TRUE ;
Time: 44.605 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00923 ; 2 - 0.07363 ; 3 - -0.0017 ; 4 - 0 ; 5 - -0.07275 ; 6 - 0 ; 7 - -0.22558 ; 8 - 0 ; 9 - -0.18518 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 25 ;
Converged: TRUE ;
Time: 56.033 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00258 ; 2 - 0 ; 3 - 0.01127 ; 4 - 3e-05 ; 5 - -0.03564 ; 6 - -1e-05 ; 7 - -0.14364 ; 8 - 0 ; 9 - -0.08738 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9980103 ;
Number of iterations: 22 ;
Converged: TRUE ;
Time: 49.018 Seconds;
Normalized w: 0 - 1 ; 1 - 0.0043 ; 2 - 0.07828 ; 3 - 0.03325 ; 4 - 0 ; 5 - 0.01107 ; 6 - 0 ; 7 - -0.0867 ; 8 - 0 ; 9 - -0.08667 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9984696 ;
Number of iterations: 23 ;
Converged: TRUE ;
Time: 50.62 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02119 ; 2 - 0.02106 ; 3 - -0.02323 ; 4 - 0 ; 5 - -0.07185 ; 6 - 0 ; 7 - -0.09448 ; 8 - 0 ; 9 - -0.01007 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 33 ;
Converged: TRUE ;
Time: 72.457 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00756 ; 2 - 0.04672 ; 3 - -0.03642 ; 4 - -1e-05 ; 5 - -0.1055 ; 6 - 0 ; 7 - -0.04511 ; 8 - 0 ; 9 - -0.0273 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 36.679 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00813 ; 2 - 3e-05 ; 3 - -0.00849 ; 4 - 0 ; 5 - -0.09853 ; 6 - 0 ; 7 - -0.13949 ; 8 - 0 ; 9 - -0.07053 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9978326 ;
Number of iterations: 40 ;
Converged: TRUE ;
Time: 85.248 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01623 ; 2 - 8e-05 ; 3 - -0.0519 ; 4 - 0 ; 5 - -0.01264 ; 6 - 0 ; 7 - 0.04119 ; 8 - 0 ; 9 - 0.02615 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 29 ;
Converged: TRUE ;
Time: 68.736 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02748 ; 2 - 0.09832 ; 3 - -0.02713 ; 4 - 0 ; 5 - -0.10309 ; 6 - -1e-05 ; 7 - -0.16247 ; 8 - 0 ; 9 - -0.13857 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 30 ;
Converged: TRUE ;
Time: 65.451 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01754 ; 2 - 0.05134 ; 3 - -0.04266 ; 4 - 0 ; 5 - -0.02455 ; 6 - 0 ; 7 - 0.03403 ; 8 - 0 ; 9 - 0.08948 ; 10 - 0 ;

Medium effects \(g_m\)

g = g.m.n

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9902233 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 46.249 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02208 ; 2 - -2e-05 ; 3 - -0.06 ; 4 - 2e-05 ; 5 - -0.03107 ; 6 - 0 ; 7 - -0.02489 ; 8 - 0 ; 9 - -0.01148 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 16 ;
Converged: TRUE ;
Time: 35.805 Seconds;
Normalized w: 0 - 1 ; 1 - -0.001 ; 2 - -0.00017 ; 3 - 0.02575 ; 4 - 4e-05 ; 5 - 0.08524 ; 6 - 0 ; 7 - 0.07865 ; 8 - 0 ; 9 - -0.01275 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 24 ;
Converged: TRUE ;
Time: 52.165 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01487 ; 2 - -0.00044 ; 3 - 0.04549 ; 4 - 0.01558 ; 5 - 0.12338 ; 6 - -1e-05 ; 7 - 0.03164 ; 8 - 0 ; 9 - -0.02527 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9980103 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 33.236 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00163 ; 2 - -5e-05 ; 3 - 0.01494 ; 4 - 0 ; 5 - 0.10446 ; 6 - 0 ; 7 - 0.13601 ; 8 - 0 ; 9 - 0.02826 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9984696 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 45.343 Seconds;
Normalized w: 0 - 1 ; 1 - -0.03071 ; 2 - -3e-05 ; 3 - -0.08536 ; 4 - 6e-05 ; 5 - -0.03201 ; 6 - 0 ; 7 - 0.20664 ; 8 - 0 ; 9 - 0.17009 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 40.944 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00452 ; 2 - 0.00964 ; 3 - -0.01881 ; 4 - -1e-05 ; 5 - 0.04503 ; 6 - 0 ; 7 - 0.04981 ; 8 - 0 ; 9 - -0.03993 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 26.82 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02488 ; 2 - 2e-05 ; 3 - 0.01352 ; 4 - 0 ; 5 - -0.10407 ; 6 - 0 ; 7 - -0.14884 ; 8 - 0 ; 9 - -0.06936 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9978326 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 33.942 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00039 ; 2 - -2e-05 ; 3 - -0.19796 ; 4 - 0.00308 ; 5 - -0.45279 ; 6 - -1e-05 ; 7 - -0.52403 ; 8 - 0 ; 9 - -0.24121 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 39.492 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00334 ; 2 - 0.01903 ; 3 - -0.04613 ; 4 - -2e-05 ; 5 - -0.04523 ; 6 - 0 ; 7 - -0.02306 ; 8 - 0 ; 9 - -0.02637 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 21 ;
Converged: TRUE ;
Time: 46.043 Seconds;
Normalized w: 0 - 1 ; 1 - -0.00574 ; 2 - 0.02839 ; 3 - 0.05334 ; 4 - -1e-05 ; 5 - 0.24599 ; 6 - 0 ; 7 - 0.31199 ; 8 - 0 ; 9 - 0.18351 ; 10 - 0 ;

Large effects \(g_l\)

g = g.l.n

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9902233 ;
Number of iterations: 10 ;
Converged: TRUE ;
Time: 23.547 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00127 ; 2 - -2e-05 ; 3 - 0.01332 ; 4 - 1e-05 ; 5 - -0.0247 ; 6 - -1e-05 ; 7 - -0.067 ; 8 - 0 ; 9 - -0.07781 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 34.477 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02673 ; 2 - -0.0642 ; 3 - -0.01243 ; 4 - 1e-05 ; 5 - 0.05384 ; 6 - 0 ; 7 - 0.167 ; 8 - 0 ; 9 - 0.12692 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 15 ;
Converged: TRUE ;
Time: 36.827 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02715 ; 2 - -0.01423 ; 3 - -0.03419 ; 4 - 1e-05 ; 5 - 0.03602 ; 6 - 0 ; 7 - 0.0863 ; 8 - 0 ; 9 - 0.09391 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9980103 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 28.188 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01619 ; 2 - -4e-05 ; 3 - -0.12451 ; 4 - -6e-05 ; 5 - -0.32621 ; 6 - 1e-05 ; 7 - -0.35849 ; 8 - 0 ; 9 - -0.17387 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9984696 ;
Number of iterations: 11 ;
Converged: TRUE ;
Time: 26.829 Seconds;
Normalized w: 0 - 1 ; 1 - -0.02534 ; 2 - -5e-05 ; 3 - -0.07491 ; 4 - 0.0087 ; 5 - -0.06932 ; 6 - -2e-05 ; 7 - 0.0128 ; 8 - 0 ; 9 - 0.07562 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 27.918 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02581 ; 2 - -3e-05 ; 3 - 0.00547 ; 4 - 0 ; 5 - 0.05689 ; 6 - 0 ; 7 - 0.15519 ; 8 - 0 ; 9 - 0.04178 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 18 ;
Converged: TRUE ;
Time: 43.267 Seconds;
Normalized w: 0 - 1 ; 1 - 0.00935 ; 2 - -0.04827 ; 3 - 0.0594 ; 4 - 7e-05 ; 5 - 0.10376 ; 6 - 0 ; 7 - 0.04587 ; 8 - 0 ; 9 - -0.01913 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 1 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 0.9978326 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 28.254 Seconds;
Normalized w: 0 - 1 ; 1 - 0.02445 ; 2 - -1e-04 ; 3 - 0.03713 ; 4 - 0.00025 ; 5 - 0.29556 ; 6 - -1e-05 ; 7 - 0.48963 ; 8 - 0 ; 9 - 0.25737 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 28.116 Seconds;
Normalized w: 0 - 1 ; 1 - -0.01647 ; 2 - 0.0138 ; 3 - -0.07328 ; 4 - -2e-05 ; 5 - -0.00216 ; 6 - 0 ; 7 - 0.12845 ; 8 - 0 ; 9 - 0.09754 ; 10 - 0 ;

Data Set NA ;
For the Correlated Null Z Scores Only:
Number of False Discoveries by BH at FDR = 0.05: 0 ;
Number of False Discoveries by ASH at lfsr <= 0.05: 0 ;
pihat0 by ASH: 1 ;
Number of iterations: 12 ;
Converged: TRUE ;
Time: 27.507 Seconds;
Normalized w: 0 - 1 ; 1 - 0.01377 ; 2 - 0.01957 ; 3 - 0.07945 ; 4 - -2e-05 ; 5 - 0.12671 ; 6 - 0 ; 7 - 0.07457 ; 8 - 0 ; 9 - 0.06591 ; 10 - 0 ;

Session information

sessionInfo()

R version 3.3.3 (2017-03-06)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: macOS Sierra 10.12.4

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] Rmosek_7.1.3      PolynomF_0.94     cvxr_0.0.0.9009   REBayes_0.62     
[5] Matrix_1.2-8      SQUAREM_2016.10-1 EQL_1.0-0         ttutils_1.0-1    
[9] ashr_2.1-12      

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.10      knitr_1.15.1      magrittr_1.5     
 [4] MASS_7.3-45       doParallel_1.0.10 pscl_1.4.9       
 [7] lattice_0.20-34   foreach_1.4.3     stringr_1.2.0    
[10] tools_3.3.3       parallel_3.3.3    grid_3.3.3       
[13] git2r_0.18.0      htmltools_0.3.5   iterators_1.0.8  
[16] yaml_2.1.14       rprojroot_1.2     digest_0.6.11    
[19] codetools_0.2-15  evaluate_0.10     rmarkdown_1.3    
[22] stringi_1.1.2     backports_1.0.5   truncnorm_1.0-7

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Regularization of \(w\): Simulated True Effects with Homoscedastic Correlated Noises

Lei Sun

2017-05-11

Introduction

The model

Uniform mixture prior

Normal mixture prior

The data

Category I: Typical

Global null \(g_n\)

Small effects \(g_s\)

Medium effects \(g_m\)

Large effects \(g_l\)

Category II: Hostile

Global null \(g_n\)

Small effects \(g_s\)

Medium effects \(g_m\)

Large effects \(g_l\)

Category III: Friendly

Global null \(g_n\)

Small effects \(g_s\)

Medium effects \(g_m\)

Large effects \(g_l\)

Category III: iid

Global null \(g_n\)

Small effects \(g_s\)

Medium effects \(g_m\)

Large effects \(g_l\)

Session information