Posterior predictive checking demo
Light speed example with poorly chosen test statistic
ggplot2 is used for plotting, tidyr for manipulating data frames
library(ggplot2)
theme_set(theme_minimal())
library(tidyr)
library(latex2exp)
library(rprojroot)
root<-has_file(".BDA_R_demos_root")$make_fix_file()
Data
y <- read.table(root("demos_ch6","light.txt"))$V1
Sufficient statistics
n <- length(y)
s <- sd(y)
my <- mean(y)
Replicated data
sampt <- replicate(1000, rt(n, n-1)*sqrt(1+1/n)*s+my) %>%
as.data.frame()
Test statistic here is variance, which is not a good choice as the model has variance parameter and the posterior of that parameter has been updated by the same data used now in checking.
sampt_vars <- data.frame(x = sapply(sampt, var))
Plot test statistics for the data and replicates. Vertical line corresponds to the original data, and the histogram to the replicate data.
title1 <- 'Light speed example with poorly chosen test statistic
Pr(T(yrep,theta) <= T(y,theta)|y)=0.42'
ggplot(data = sampt_vars) +
geom_histogram(aes(x = x), fill = 'steelblue',
color = 'black', binwidth = 6) +
geom_vline(aes(xintercept = x), data = data.frame(x = s^2),
color = 'red') +
labs(x = TeX('Variance of \\mathit{y} and \\mathit{y}^{\\mathrm{rep}}'),
y = '', title = title1) +
scale_y_continuous(breaks=NULL)
![](data:image/png;base64,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)
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