Simulation with Realistic Standard Error: Small SNR

Introduction

Identifiability of small effects from correlation.

library(ashr)
library(edgeR)
library(limma)
library(pROC)

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

Read in data

data = readRDS("../data/liver.rds")
ngene = 1e4
data = top_gene_selection(ngene, data)$data

SNR = -10, Sparse mixture

\[g = 0.9\delta_0 + 0.1N\left(0, \sigma^2\right) \ .\]

SNR = -10, Sparse & strong

\[g = 0.99\delta_0 + 0.01N\left(0, \left(3.16\sigma\right)^2\right) \ .\]

SNR = -10, Dense & weak

\[g = 0.1\delta_0 + 0.9N\left(0, \left(0.33\sigma\right)^2\right) \ .\]

SNR = -3, Sparse mixture

\[g = 0.5\delta_0 + 0.5N\left(0, \sigma^2\right) \ .\]

SNR = -3, Sparse & strong

\[g = 0.6\delta_0 + 0.3N\left(0, \left(0.82\sigma\right)^2\right) + 0.1N\left(0, \left(1.73\sigma\right)^2\right) \ .\]

SNR = -3, Dense & weak

\[g = 0.1\delta_0 + 0.9N\left(0, \left(0.75\sigma^2\right)^2\right) \ .\]

Session information

sessionInfo()

R version 3.4.2 (2017-09-28)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Sierra 10.12.6

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     

loaded via a namespace (and not attached):
 [1] compiler_3.4.2  backports_1.1.1 magrittr_1.5    rprojroot_1.2  
 [5] tools_3.4.2     htmltools_0.3.6 yaml_2.1.14     Rcpp_0.12.13   
 [9] stringi_1.1.5   rmarkdown_1.6   knitr_1.17      git2r_0.19.0   
[13] stringr_1.2.0   digest_0.6.12   evaluate_0.10.1