Posterior predictive checking demo
Checking the assumption of independence in binomial trials (BDA3 p. 147)
ggplot2 is used for plotting, tidyr for manipulating data frames
library(ggplot2)
theme_set(theme_minimal())
library(tidyr)
library(latex2exp)
Data
y <- c(1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0)
Compute test statistic for the data. Test statistic is the number of switches from 0 to 1 or from 1 to 0.
Ty <- sum(diff(y) != 0) + 0.0
Sufficient statistics
n <- length(y)
s <- sum(y)
Compute test statistic for the replicate data.
rb <- function(s, n) {
p <- rbeta(1, s+1, n-s+1)
yr <- rbinom(n, 1, p)
sum(diff(yr) != 0) + 0.0
}
Tyr <- data.frame(x = replicate(10000, rb(s, n)))
Compute posterior predictive p-value
mean(Tyr<=Ty)
## [1] 0.0305
Plot test statistics for the data and replicates. Vertical line corresponds to the original data, and the histogram to the replicate data.
title1 <- 'Binomial example - number of changes?
Pr(T(yrep,theta) <= T(y,theta)|y) = 0.03'
ggplot(data = Tyr) +
geom_histogram(aes(x = x), fill = 'steelblue',
color = 'black', binwidth = 1) +
geom_vline(aes(xintercept = x), data = data.frame(x = Ty),
color = 'red') +
labs(x = TeX(r"(Number of changes in $\textit{y}$ and $\textit{y}^{ \textrm{rep}}$)"),
y = '', title = title1) +
scale_y_continuous(breaks=NULL)
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)
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