The correlated $N(0, 1)$ figure in `cashr`

Last updated: 2018-10-07

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Introduction

Document the correlated $N(0, 1)$ figure in the cashr paper.

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

Loading required package: EQL

Loading required package: ttutils

Loading required package: SQUAREM

Loading required package: REBayes

Loading required package: Matrix

Loading required package: CVXR


Attaching package: 'CVXR'

The following object is masked from 'package:stats':

    power

Loading required package: PolynomF

Warning: package 'PolynomF' was built under R version 3.4.4

Loading required package: Rmosek

Loading required package: ashr


Attaching package: 'ashr'

The following object is masked from 'package:CVXR':

    get_np

source("../code/gdfit.R")
z.mat <- readRDS("../output/z_null_liver_777.rds")
sel = c(32, 327, 355, 483)
z.sel <- z.mat[sel, ]
gd.ord <- 10

x.plot = seq(- max(abs(z.sel)) - 2, max(abs(z.sel)) + 2, length = 1000)
hermite = Hermite(gd.ord)
gd0.std = dnorm(x.plot)
matrix_lik_plot = cbind(gd0.std)
for (j in 1 : gd.ord) {
  gd.std = (-1)^j * hermite[[j]](x.plot) * gd0.std / sqrt(factorial(j))
  matrix_lik_plot = cbind(matrix_lik_plot, gd.std)
}

z = z.sel[4, ]
w <- gdfit(z, gd.ord, w.lambda = 10, w.rho = 0.5)$w
y.plot = matrix_lik_plot %*% w
z.hist = hist(z, breaks = 100, plot = FALSE)
y.max = max(z.hist$density, y.plot, dnorm(0))

setEPS()
postscript("../output/paper/cor_z_hist.eps", width = 8, height = 6)
#pdf("../output/paper/cor_z_hist.pdf", width = 8, height = 6)

par(mfrow = c(2, 2)) # 2-by-2 grid of plots
par(oma = c(0.5, 2.5, 0, 0)) # make room (i.e. the 4's) for the overall x and y axis titles
par(mar = c(2, 2, 3.5, 1)) # make the plots be closer together

# now plot the graphs with the appropriate axes removed (via xaxt and yaxt),
# remove axis labels (so that they are not redundant with overall labels,
# and set some other nice choices for graphics parameters
for (i in 1 : 4) {
  z = z.sel[i, ]
  w <- gdfit(z, gd.ord)$w
  y.plot = matrix_lik_plot %*% w
  z.hist = hist(z, breaks = 100, plot = FALSE)
  hist(z, breaks = 100, prob = TRUE, ylim = c(0, y.max), main = NULL, xlab = "", xlim = range(c(abs(z.sel), -abs(z.sel))))
  lines(x.plot, dnorm(x.plot), col = "blue", lwd = 2)
  lines(x.plot, y.plot, col = "red", lwd = 2)
  legend("topleft", bty = "n", paste0('(', letters[i], ')'), cex = 1.25)
}

# print the overall labels
mtext('Density', side = 2, outer = TRUE, line = 1)
mtext("Histograms of Correlated N(0,1) Variates", line = -2, outer = TRUE)

legend("topleft", inset = c(-0.65, -0.25), legend = c("N(0, 1)", "Gaussian Derivatives"), lty = 1, lwd = 2, xpd = NA, col = c("blue", "red"), ncol = 2)

dev.off()

quartz_off_screen 
                2

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 10.13.6

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     

other attached packages:
[1] ashr_2.2-3        Rmosek_8.0.69     PolynomF_1.0-2    CVXR_0.99        
[5] REBayes_1.2       Matrix_1.2-12     SQUAREM_2017.10-1 EQL_1.0-0        
[9] ttutils_1.0-1    

loaded via a namespace (and not attached):
 [1] gmp_0.5-13.2      Rcpp_0.12.18      compiler_3.4.3   
 [4] git2r_0.21.0      workflowr_1.1.1   R.methodsS3_1.7.1
 [7] R.utils_2.7.0     iterators_1.0.9   tools_3.4.3      
[10] digest_0.6.15     bit_1.1-12        evaluate_0.10.1  
[13] lattice_0.20-35   foreach_1.4.4     yaml_2.1.18      
[16] parallel_3.4.3    Rmpfr_0.7-1       ECOSolveR_0.4    
[19] stringr_1.3.0     knitr_1.20        rprojroot_1.3-2  
[22] bit64_0.9-7       grid_3.4.3        R6_2.2.2         
[25] rmarkdown_1.9     magrittr_1.5      whisker_0.3-2    
[28] MASS_7.3-50       backports_1.1.2   codetools_0.2-15 
[31] htmltools_0.3.6   scs_1.1-1         stringi_1.1.6    
[34] pscl_1.5.2        doParallel_1.0.11 truncnorm_1.0-7  
[37] R.oo_1.22.0

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The correlated \(N(0, 1)\) figure in `cashr`

Lei Sun

2018-10-03

Introduction

Session information

The correlated \(N(0, 1)\) figure in cashr

Lei Sun

2018-10-03

Introduction

Session information

The correlated \(N(0, 1)\) figure in `cashr`