CASH Simulation, Part 6: Simulated vs Read data

Simulated correlated data

\[ z_i = L_i^Tx / \sqrt{L_i^TL_i} \ , \] where both \(x\) and \(L_i\) are \(d\)-dimentional independent \(N(0,1)\) random variates, and a large number of \(z_i\) are generated by the same \(x\) and different, independent \(L_i\).

Observation

After extensive exploratory simulations, it seems completely simulated data give cleaner results than simulated real data, which is expected.

source("../code/gdash_lik.R")

set.seed(777)
z.mat <- se.mat <- matrix(0, ncol = 1e4, nrow = 1e3)
for (i in 1 : nrow(z.mat)) {
  L <- matrix(rnorm(1e4 * 10), ncol = 10)
  z.mat[i, ] <- L %*% rnorm(10) / sqrt(rowSums(L^2))
  se.mat[i, ] <- sqrt(rchisq(1e4, 1))
}

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.5, 0.3, 0.2), g.sd = c(0, 1, 2), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.5, 0.4, 0.1), g.sd = c(0, 1, 2), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.6, 0.3, 0.1), g.sd = c(0, 1, 2), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.1), g.sd = c(0, 1), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.1), g.sd = c(0, 2), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.1), g.sd = c(0, 3), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.05, 0.05), g.sd = c(0, 1, 2), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.05, 0.05), g.sd = c(0, 1, 3), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.5, 0.5), g.sd = c(0, 1), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.5, 0.5), g.sd = c(0, 2), relative_to_noise = FALSE)

Simulation

cashSim(z.mat, se.mat,
        nsim = 200, ngene = 1000,
        g.pi = c(0.5, 0.5), g.sd = c(0, 3), relative_to_noise = FALSE)

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol

Read data

z.real <- readRDS("../output/z_null_liver_777.rds")
se.real <- readRDS("../output/sebetahat_null_liver_777.rds")

Simulation

cashSim(z.real, se.real,
        nsim = 200, ngene = 1000,
        g.pi = c(0.5, 0.5), g.sd = c(0, 1), relative_to_noise = TRUE)

Simulation

cashSim(z.real, se.real,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.1), g.sd = c(0, 1), relative_to_noise = TRUE)

Simulation

cashSim(z.real, se.real,
        nsim = 200, ngene = 1000,
        g.pi = c(0.9, 0.1), g.sd = c(0, 2), relative_to_noise = TRUE)

Session information

sessionInfo()

R version 3.4.2 (2017-09-28)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.1

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib

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] ashr_2.1-27       Rmosek_7.1.3      PolynomF_0.94     cvxr_0.0.0.9009  
[5] REBayes_0.85      Matrix_1.2-11     SQUAREM_2017.10-1 EQL_1.0-0        
[9] ttutils_1.0-1    

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.13      knitr_1.17        magrittr_1.5     
 [4] MASS_7.3-47       pscl_1.5.2        doParallel_1.0.11
 [7] lattice_0.20-35   foreach_1.4.3     stringr_1.2.0    
[10] tools_3.4.2       parallel_3.4.2    grid_3.4.2       
[13] git2r_0.19.0      iterators_1.0.8   htmltools_0.3.6  
[16] yaml_2.1.14       rprojroot_1.2     digest_0.6.12    
[19] codetools_0.2-15  evaluate_0.10.1   rmarkdown_1.6    
[22] stringi_1.1.5     compiler_3.4.2    backports_1.1.1  
[25] truncnorm_1.0-7