Last updated: 2017-03-07

Code version: 03366d9

Introduction

Following previous simulation on randomly selected data sets, this time we first apply ash on \(z\) scores for every data set, and take a second look at those data sets on which ash makes most mistakes, or in other words, produces smallest \(\hat\pi_0\).

Simulation and ash

z = read.table("../output/z_null_liver_777.txt")
library(ashr)
n = dim(z)[1]
pihat0 = c()
for (i in 1:n) {
  ash.fit = ash(as.numeric(z[i, ]), 1, method = "fdr")
  pihat0[i] = get_pi0(ash.fit)
}

Histograms of \(z\) scores in 100 most “ash-hostile” data sets

I = order(pihat0)[1:100]
x = seq(-10, 10, 0.01)
y = dnorm(x)
k = 1
for (j in I) {
  cat("N0.", k, ": Data Set", j, "pihat0 =", pihat0[j])
  hist(as.numeric(z[j, ]), xlab = "z scores", freq = FALSE, ylim = c(0, 0.45), main = "10000 z scores, default")
  lines(x, y, col = "red")
  hist(as.numeric(z[j, ]), xlab = "z scores", freq = FALSE, ylim = c(0, 0.45), nclass = 100, main = "10000 z scores, 100 bins")
  lines(x, y, col = "red")
  k = k + 1
}
N0. 1 : Data Set 724 pihat0 = 0.01606004

N0. 2 : Data Set 33 pihat0 = 0.01680632

N0. 3 : Data Set 537 pihat0 = 0.01681555

N0. 4 : Data Set 522 pihat0 = 0.02083846

N0. 5 : Data Set 693 pihat0 = 0.02122591

N0. 6 : Data Set 840 pihat0 = 0.02316832

N0. 7 : Data Set 749 pihat0 = 0.02583276

N0. 8 : Data Set 269 pihat0 = 0.02787007

N0. 9 : Data Set 360 pihat0 = 0.0308234

N0. 10 : Data Set 23 pihat0 = 0.03139009

N0. 11 : Data Set 389 pihat0 = 0.03156173

N0. 12 : Data Set 923 pihat0 = 0.03239883

N0. 13 : Data Set 22 pihat0 = 0.03271534

N0. 14 : Data Set 885 pihat0 = 0.03413736

N0. 15 : Data Set 705 pihat0 = 0.03438913

N0. 16 : Data Set 40 pihat0 = 0.03668824

N0. 17 : Data Set 338 pihat0 = 0.0393062

N0. 18 : Data Set 379 pihat0 = 0.03958053

N0. 19 : Data Set 649 pihat0 = 0.04041784

N0. 20 : Data Set 627 pihat0 = 0.04041922

N0. 21 : Data Set 133 pihat0 = 0.04064386

N0. 22 : Data Set 915 pihat0 = 0.04083527

N0. 23 : Data Set 999 pihat0 = 0.04218153

N0. 24 : Data Set 182 pihat0 = 0.04223457

N0. 25 : Data Set 511 pihat0 = 0.04232901

N0. 26 : Data Set 122 pihat0 = 0.04301549

N0. 27 : Data Set 937 pihat0 = 0.04305909

N0. 28 : Data Set 771 pihat0 = 0.04316169

N0. 29 : Data Set 495 pihat0 = 0.04395344

N0. 30 : Data Set 41 pihat0 = 0.04491135

N0. 31 : Data Set 984 pihat0 = 0.04567195

N0. 32 : Data Set 3 pihat0 = 0.0465218

N0. 33 : Data Set 907 pihat0 = 0.04653847

N0. 34 : Data Set 355 pihat0 = 0.04750946

N0. 35 : Data Set 485 pihat0 = 0.04794909

N0. 36 : Data Set 56 pihat0 = 0.04829662

N0. 37 : Data Set 809 pihat0 = 0.04880257

N0. 38 : Data Set 404 pihat0 = 0.05059485

N0. 39 : Data Set 858 pihat0 = 0.05110069

N0. 40 : Data Set 77 pihat0 = 0.05151585

N0. 41 : Data Set 800 pihat0 = 0.05218407

N0. 42 : Data Set 562 pihat0 = 0.05247834

N0. 43 : Data Set 893 pihat0 = 0.05252202

N0. 44 : Data Set 403 pihat0 = 0.0531628

N0. 45 : Data Set 780 pihat0 = 0.05426134

N0. 46 : Data Set 538 pihat0 = 0.05493143

N0. 47 : Data Set 324 pihat0 = 0.05506971

N0. 48 : Data Set 176 pihat0 = 0.05513259

N0. 49 : Data Set 972 pihat0 = 0.05539611

N0. 50 : Data Set 644 pihat0 = 0.0557842

N0. 51 : Data Set 977 pihat0 = 0.0564768

N0. 52 : Data Set 467 pihat0 = 0.06112237

N0. 53 : Data Set 857 pihat0 = 0.06183555

N0. 54 : Data Set 783 pihat0 = 0.06208376

N0. 55 : Data Set 976 pihat0 = 0.06343862

N0. 56 : Data Set 968 pihat0 = 0.06385437

N0. 57 : Data Set 942 pihat0 = 0.06399678

N0. 58 : Data Set 402 pihat0 = 0.06468693

N0. 59 : Data Set 341 pihat0 = 0.06681535

N0. 60 : Data Set 411 pihat0 = 0.06812445

N0. 61 : Data Set 484 pihat0 = 0.06857855

N0. 62 : Data Set 476 pihat0 = 0.06944478

N0. 63 : Data Set 407 pihat0 = 0.07139176

N0. 64 : Data Set 871 pihat0 = 0.07236197

N0. 65 : Data Set 638 pihat0 = 0.07281058

N0. 66 : Data Set 232 pihat0 = 0.07317683

N0. 67 : Data Set 778 pihat0 = 0.07619716

N0. 68 : Data Set 349 pihat0 = 0.07627442

N0. 69 : Data Set 985 pihat0 = 0.07865805

N0. 70 : Data Set 259 pihat0 = 0.0794454

N0. 71 : Data Set 452 pihat0 = 0.079703

N0. 72 : Data Set 268 pihat0 = 0.08182634

N0. 73 : Data Set 526 pihat0 = 0.08340671

N0. 74 : Data Set 274 pihat0 = 0.08580661

N0. 75 : Data Set 685 pihat0 = 0.08592309

N0. 76 : Data Set 499 pihat0 = 0.08826948

N0. 77 : Data Set 982 pihat0 = 0.08854547

N0. 78 : Data Set 582 pihat0 = 0.08899861

N0. 79 : Data Set 953 pihat0 = 0.08900989

N0. 80 : Data Set 811 pihat0 = 0.08962902

N0. 81 : Data Set 575 pihat0 = 0.0946117

N0. 82 : Data Set 997 pihat0 = 0.09560788

N0. 83 : Data Set 231 pihat0 = 0.09686204

N0. 84 : Data Set 781 pihat0 = 0.09690435

N0. 85 : Data Set 853 pihat0 = 0.09889116

N0. 86 : Data Set 868 pihat0 = 0.09918104

N0. 87 : Data Set 502 pihat0 = 0.1001788

N0. 88 : Data Set 606 pihat0 = 0.1033893

N0. 89 : Data Set 912 pihat0 = 0.106048

N0. 90 : Data Set 659 pihat0 = 0.1065714

N0. 91 : Data Set 501 pihat0 = 0.1090034

N0. 92 : Data Set 296 pihat0 = 0.1115216

N0. 93 : Data Set 895 pihat0 = 0.1119629

N0. 94 : Data Set 153 pihat0 = 0.1148195

N0. 95 : Data Set 477 pihat0 = 0.1172838

N0. 96 : Data Set 769 pihat0 = 0.1187511

N0. 97 : Data Set 555 pihat0 = 0.1210902

N0. 98 : Data Set 475 pihat0 = 0.1273824

N0. 99 : Data Set 584 pihat0 = 0.1291777

N0. 100 : Data Set 949 pihat0 = 0.1308901

Session Information

sessionInfo()
R version 3.3.2 (2016-10-31)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: macOS Sierra 10.12.3

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     

loaded via a namespace (and not attached):
 [1] backports_1.0.5 magrittr_1.5    rprojroot_1.2   tools_3.3.2    
 [5] htmltools_0.3.5 yaml_2.1.14     Rcpp_0.12.9     stringi_1.1.2  
 [9] rmarkdown_1.3   knitr_1.15.1    git2r_0.18.0    stringr_1.1.0  
[13] digest_0.6.9    workflowr_0.3.0 evaluate_0.10

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