Last updated: 2018-05-15

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Introduction

varbvs.get.lfsr <- function (fit) {

# For each variable, and each hyperparameter setting, get the
# posterior probability that the regression coefficient is exactly
# zero.
p0 <- 1 - fit$alpha

# For each variable, and for each hyperparameter setting, get the
# posterior probability that the regression coefficient is negative.
pn <- with(fit,alpha * pnorm(0,mu,sqrt(s)))

# For each variable, and for each hyperparameter setting, ompute the
# local false sign rate (LFSR) following the formula given in
# Matthew's Biostatistics paper, "False discovery rates: a new deal".
p        <- nrow(fit$alpha)
k          <- ncol(fit$alpha)
lfsr     <- matrix(0,p,k)
b        <- pn > 0.5*(1 - p0)
lfsr[b]  <- 1 - pn[b]
lfsr[!b] <- p0[!b] + pn[!b]

# Average the average LFSR over the hyperparameter settings, weighted
# by the probability of each hyperparameter setting.
lfsr <-    c(lfsr %*% fit$w)

return(lfsr)
}

\(n > p\)

n <- 1200
p <- 1000
k <- 50
m <- 100
q <- 0.1

Independent design

\(X_{n \times p}\) has independent columns simulated from \(N(0, (1/\sqrt n)^2)\) so they are roughly normalized.

Cov.X <- diag(1 / n, p)

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Local correlation / AR model for \(X\)

\(X_{n \times p}\) has correlation \(\Sigma_{ij} = \rho^{|i - j|}\). Each row is independently \(N(0, \frac1n\Sigma)\).

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Factor Model for \(X\)

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Factor Model for \(\hat\beta\)

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\(n < p\)

n <- 300
p <- 1000
k <- 50
m <- 100
q <- 0.1

Independent design

Cov.X <- diag(1 / n, p)

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Local correlation / AR model for \(X\)

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Factor Model for \(X\)

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Factor Model for \(\hat\beta\)

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Session information

sessionInfo()
R version 3.4.3 (2017-11-30)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.4

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] parallel  stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
[1] lattice_0.20-35 doMC_1.3.5      iterators_1.0.9 foreach_1.4.4  
[5] ggplot2_2.2.1   reshape2_1.4.3  Matrix_1.2-12   varbvs_2.5-2   
[9] knockoff_0.3.0 

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.16        compiler_3.4.3      pillar_1.0.1       
 [4] RColorBrewer_1.1-2  git2r_0.21.0        plyr_1.8.4         
 [7] workflowr_1.0.1     R.methodsS3_1.7.1   R.utils_2.6.0      
[10] tools_3.4.3         digest_0.6.15       evaluate_0.10.1    
[13] tibble_1.4.1        gtable_0.2.0        rlang_0.1.6        
[16] yaml_2.1.18         stringr_1.3.0       knitr_1.20         
[19] rprojroot_1.3-2     grid_3.4.3          rmarkdown_1.9      
[22] latticeExtra_0.6-28 magrittr_1.5        whisker_0.3-2      
[25] codetools_0.2-15    backports_1.1.2     scales_0.5.0       
[28] htmltools_0.3.6     colorspace_1.3-2    nor1mix_1.2-3      
[31] stringi_1.1.6       lazyeval_0.2.1      munsell_0.4.3      
[34] R.oo_1.21.0

This reproducible R Markdown analysis was created with workflowr 1.0.1