CASH on FDR, 1

Introduction

The model is

\[ \beta_j \sim g(\cdot) \ ;\\ \hat\beta_j = \beta_j + \hat s_j z_j \ ;\\ z_j \sim N(0, 1) \ , \] where \[ g = 0.5\delta_0 + 0.5N(0, \sigma_n^2) \ . \] We consider three scenarios for the noise \(z_j\): 1. Correlated noise, simulated from real data; 2. Independent noise; 3. Correlated noise, simulated from artificial data.

nsim <- 100
ngene <- 1000
pi0 <- 0.5
snr <- 1
FDR.nominal <- seq(0, 0.1, 0.001)[-1]

Correlated noise, real data

No id variables; using all as measure variables

Warning: Computation failed in `stat_summary()`:
object 'mean_sdp' of mode 'function' was not found

Warning: Computation failed in `stat_summary()`:
object 'mean_sdp' of mode 'function' was not found

Warning: Computation failed in `stat_summary()`:
object 'mean_sdp' of mode 'function' was not found

Warning: Computation failed in `stat_summary()`:
object 'mean_sdp' of mode 'function' was not found

Independent data

Correlated, synthetic data

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] edgeR_3.20.1      limma_3.34.0      ggplot2_2.2.1    
 [4] reshape2_1.4.2    ashr_2.1-27       Rmosek_7.1.3     
 [7] PolynomF_0.94     cvxr_0.0.0.9009   REBayes_0.85     
[10] Matrix_1.2-11     SQUAREM_2017.10-1 EQL_1.0-0        
[13] ttutils_1.0-1    

loaded via a namespace (and not attached):
 [1] qvalue_2.10.0       locfit_1.5-9.1      splines_3.4.2      
 [4] lattice_0.20-35     colorspace_1.3-2    htmltools_0.3.6    
 [7] yaml_2.1.14         base64enc_0.1-3     survival_2.41-3    
[10] rlang_0.1.4         foreign_0.8-69      RColorBrewer_1.1-2 
[13] foreach_1.4.3       plyr_1.8.4          stringr_1.2.0      
[16] munsell_0.4.3       gtable_0.2.0        htmlwidgets_0.9    
[19] codetools_0.2-15    evaluate_0.10.1     labeling_0.3       
[22] latticeExtra_0.6-28 knitr_1.17          pscl_1.5.2         
[25] doParallel_1.0.11   parallel_3.4.2      htmlTable_1.9      
[28] Rcpp_0.12.13        acepack_1.4.1       checkmate_1.8.5    
[31] scales_0.5.0        backports_1.1.1     Hmisc_4.0-3        
[34] truncnorm_1.0-7     gridExtra_2.3       digest_0.6.12      
[37] stringi_1.1.5       grid_3.4.2          rprojroot_1.2      
[40] tools_3.4.2         magrittr_1.5        lazyeval_0.2.1     
[43] tibble_1.3.4        Formula_1.2-2       cluster_2.0.6      
[46] MASS_7.3-47         data.table_1.10.4-3 assertthat_0.2.0   
[49] rmarkdown_1.6       iterators_1.0.8     rpart_4.1-11       
[52] nnet_7.3-12         git2r_0.19.0        compiler_3.4.2