Figure to show average empirical CDF is $N(0,1)$

Last updated: 2018-12-14

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Unstaged changes:
    Modified:   analysis/cash_plots_2.rmd

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File	Version	Author	Date	Message
rmd	27a4a50	Lei Sun	2018-11-11	average emp cdf fight

# source("../code/count_to_summary.R")
# 
# r <- readRDS("../data/liver.rds")
# ngene <- 1e4
# 
# Y = lcpm(r)
# subset = top_genes_index(ngene, Y)
# r = r[subset,]
# 
# nsamp <- 5
# set.seed(7)
# nsim <- 1e4
# Z.list <- W <- list()
# for (i in 1 : nsim) {
#   ## generate data
#   counts <- r[, sample(ncol(r), 2 * nsamp)]
#   design <- model.matrix(~c(rep(0, nsamp), rep(1, nsamp)))
#   summary <- count_to_summary(counts, design)
#   Z <- summary$z
#   Z.list[[i]] <- Z
#   Z.GD <- gdfit.mom(Z, 100)
#   W[[i]] <- Z.GD$w
# }
# Z.gtex <- Z.list
# W.gtex <- W

Z.gtex <- readRDS('../output/paper/simulation/Z.gtex.rds')

quantile.vec1 <- exp(seq(-21, -5, by = 0.01))
quantile.vec2 <- seq(0.007, 0.993, by = 0.001)
quantile.vec3 <- exp(seq(-5, -21, by = -0.01))
emp.cdf.Z1 <- sapply(quantile.vec1, function(x) {sapply(Z.gtex, function(y) mean(y <= qnorm(x)))})
emp.cdf.Z2 <- sapply(quantile.vec2, function(x) {sapply(Z.gtex, function(y) mean(y <= qnorm(x)))})
emp.cdf.Z3 <- sapply(quantile.vec3, function(x) {sapply(Z.gtex, function(y) mean(y <= -qnorm(x)))})
emp.cdf.Z4 <- sapply(quantile.vec3, function(x) {sapply(Z.gtex, function(y) mean(y > -qnorm(x)))})

ecdf.avg1 <- colMeans(emp.cdf.Z1)
ecdf.avg2 <- colMeans(emp.cdf.Z2)
ecdf.avg3 <- colMeans(emp.cdf.Z3)
ecdf.avg4 <- colMeans(emp.cdf.Z4)
ecdf.avg <- c(ecdf.avg1, ecdf.avg2, ecdf.avg3)
ecdf.tail.avg.conf.int1 <- apply(emp.cdf.Z1, 2, function(x) {t.test(x, conf.level = 0.999)$conf.int})
ecdf.tail.avg.conf.int4 <- apply(emp.cdf.Z4, 2, function(x) {t.test(x, conf.level = 0.999)$conf.int})

pdf("../output/paper/ecdf_avg.pdf", height = 5, width = 5)
par(mar = c(4.5, 4.5, 2.5, 1))
plot(c(qnorm(quantile.vec1), qnorm(quantile.vec2), -qnorm(quantile.vec3)), ecdf.avg, type = "l", xlab = "z-scores", ylab = "CDF", cex.lab = 2, lwd = 2)
title(expression('(a): Avg. Emp. CDF'), cex.main = 2)
lines(c(qnorm(quantile.vec1), qnorm(quantile.vec2), -qnorm(quantile.vec3)), c(quantile.vec1, quantile.vec2, pnorm(-qnorm(quantile.vec3))), lty = 2, col = "blue", lwd = 2)
legend("bottomright", lty = c(1, 2), col = c(1, "blue"), legend = c(expression(bar("F"[p])), expression('N(0,1)')), lwd = 2, cex = 2, bty = 'n')
rect(xleft = c(range(qnorm(quantile.vec1))[1], range(-qnorm(quantile.vec3))[1]),
     xright = c(range(qnorm(quantile.vec1))[2], range(-qnorm(quantile.vec3))[2]),
     ybottom = c(range(quantile.vec1, ecdf.avg1)[1], range(1 - quantile.vec3, 1 - ecdf.avg4)[1]),
     ytop = c(range(quantile.vec1, ecdf.avg1)[2], range(1 - quantile.vec3, 1 - ecdf.avg4)[2]),
     border = "red", lty = c(1, 5)
     )
dev.off()

quartz_off_screen 
                2

pdf("../output/paper/ecdf_avg_left.pdf", height = 5, width = 5)
par(mar = c(4.5, 4.5, 2.5, 1))
plot(qnorm(quantile.vec1), log(ecdf.avg1), type = "l",
     ylim = range(log(quantile.vec1), log(ecdf.avg1)),
     xlab = "z-scores", ylab = "log(CDF)", bty = "n", lwd = 2, cex.lab = 2)
title(expression('(b): Left Tail'), cex.main = 2)
lines(qnorm(quantile.vec1), log(quantile.vec1), lty = 2, col = "blue", lwd = 2)
lines(qnorm(quantile.vec1), log(pnorm(qnorm(quantile.vec1), 0, 1.1)), lty = 3, col = "orange", lwd = 2)
lines(qnorm(quantile.vec1), log(pnorm(qnorm(quantile.vec1), 0, 1.05)), lty = 4, col = "green", lwd = 2)
polygon(x = c(qnorm(quantile.vec1), rev(qnorm(quantile.vec1))),
        y = c(pmax(log(pmax(ecdf.tail.avg.conf.int1, 0)[1, ]), -30), rev(log(pmax(ecdf.tail.avg.conf.int1, 0)[2, ]))),
        border = NA,
        col = grDevices::adjustcolor("grey75", alpha.f = 0.5))
legend("bottomright", lty = c(1, 2, 4, 3), col = c("black", "blue", "green", "orange"), legend = c(
  expression(bar("F"[p])),
  expression(N(0, 1)),
  expression(N(0, 1.05^2)),
  expression(N(0, 1.1^2))
), bty = 'n', lwd = 2, cex = 1.75)
box(col = "red")
dev.off()

quartz_off_screen 
                2

pdf("../output/paper/ecdf_avg_right.pdf", height = 5, width = 5)
par(mar = c(4.5, 4.5, 2.5, 1))
plot(-qnorm(quantile.vec3), log(ecdf.avg4), type = "l",
     ylim = range(log(quantile.vec3), log(ecdf.avg4)),
     xlab = "z-scores", ylab = "log(1-CDF)", bty = "n", lwd = 2, cex.lab = 2)
title(expression('(c): Right Tail'), cex.main = 2)
lines(-qnorm(quantile.vec3), log(quantile.vec3), lty = 2, col = "blue", lwd = 2)
lines(-qnorm(quantile.vec3), log(pnorm(qnorm(quantile.vec3), 0, 1.1)), lty = 3, lwd = 2, col = "orange")
lines(-qnorm(quantile.vec3), log(pnorm(qnorm(quantile.vec3), 0, 1.05)), lty = 4, lwd = 2, col = "green")
polygon(x = c(-qnorm(quantile.vec3), rev(-qnorm(quantile.vec3))),
        y = c(pmax(log(pmax(ecdf.tail.avg.conf.int4[1, ], 0)), -30), rev(log(ecdf.tail.avg.conf.int4[2, ]))),
        border = NA,
        col = grDevices::adjustcolor("grey75", alpha.f = 0.5))
legend("bottomleft", lty = c(1, 2, 4, 3), col = c("black", "blue", "green", "orange"), legend = c(
  expression(bar("F"[p])),
  expression(N(0, 1)),
  expression(N(0, 1.05^2)),
  expression(N(0, 1.1^2))
), lwd = 2, cex = 1.75, bty = 'n')
box(col = "red", lty = 5)
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  10.14.1

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     

loaded via a namespace (and not attached):
 [1] workflowr_1.1.1   Rcpp_0.12.16      digest_0.6.15    
 [4] rprojroot_1.3-2   R.methodsS3_1.7.1 backports_1.1.2  
 [7] git2r_0.23.0      magrittr_1.5      evaluate_0.10.1  
[10] stringi_1.2.2     whisker_0.3-2     R.oo_1.22.0      
[13] R.utils_2.6.0     rmarkdown_1.9     tools_3.4.3      
[16] stringr_1.3.1     yaml_2.1.19       compiler_3.4.3   
[19] htmltools_0.3.6   knitr_1.20

This reproducible R Markdown analysis was created with workflowr 1.1.1

Figure to show average empirical CDF is \(N(0,1)\)

Lei Sun

2018-11-11

Session information