Detecting model misfit with posterior predictive checks

Setup

Load packages

library(rstan)
library(ggplot2)
library(bayesplot)
theme_set(bayesplot::theme_default(base_family = "sans"))
library(loo)
library(rprojroot)
root<-has_file(".BDA_R_demos_root")$make_fix_file()

1 Load and examine data

source(root("demos_rstan/ppc", "count-data.R"))
print(N)

[1] 500

print(y)

  [1] 0 3 5 0 4 7 4 2 3 6 7 0 0 3 7 5 5 0 4 0 4 4 6 3 7 5 3 0 0 2 0 1 0 1 5 4 4
 [38] 2 3 6 4 5 0 7 7 4 4 4 0 6 1 5 6 5 6 7 3 6 2 3 0 2 0 6 6 0 3 4 4 5 5 0 5 7
 [75] 5 5 6 4 2 3 4 6 4 6 6 4 0 6 5 5 7 0 1 6 7 0 5 0 0 5 6 5 1 0 7 1 2 6 5 4 0
[112] 4 0 4 4 6 3 0 0 3 3 4 2 5 3 4 3 2 5 2 4 4 0 2 7 5 7 5 5 7 7 0 4 6 0 4 6 7
[149] 4 0 4 1 5 0 3 5 7 6 0 5 5 6 7 6 7 3 4 3 7 7 2 5 4 5 5 0 6 2 4 5 4 0 0 5 5
[186] 7 7 0 3 0 3 3 6 1 4 2 0 4 7 5 5 0 3 7 0 6 6 4 1 6 7 6 0 3 6 4 7 0 5 5 4 0
[223] 0 2 4 6 0 5 0 2 7 2 7 5 4 6 2 4 0 4 0 0 3 5 4 3 5 5 7 7 0 6 4 5 1 5 3 5 5
[260] 5 0 2 7 6 2 3 2 5 4 7 6 7 3 3 4 4 6 4 6 7 1 5 6 3 3 6 3 4 0 7 0 3 6 5 0 0
[297] 0 5 4 4 0 4 7 5 5 3 3 0 0 5 4 0 7 6 0 6 2 0 6 1 0 4 0 4 3 0 4 5 5 7 6 6 5
[334] 4 7 0 6 4 7 7 5 0 1 4 7 6 4 5 4 7 2 5 2 6 3 2 7 4 3 4 6 6 6 6 7 1 0 0 7 7
[371] 4 2 4 5 5 7 4 1 7 6 5 6 5 4 0 0 7 0 0 5 6 6 3 6 0 0 0 4 4 3 0 7 5 4 2 7 0
[408] 4 0 0 2 4 5 0 4 2 5 2 0 6 6 3 6 0 2 5 0 0 0 6 0 0 6 5 4 6 4 5 5 4 0 3 4 3
[445] 3 5 3 4 5 7 0 0 1 4 6 3 5 7 6 6 5 0 5 4 0 0 2 6 0 6 0 4 5 6 3 4 2 3 4 0 5
[482] 0 0 0 0 3 4 7 6 7 7 3 4 4 7 4 5 2 5 6

qplot(y)

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.1 Plot histogram of draws from Poisson with same mean

x <- rpois(N, mean(y))
qplot(x)

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.