demo2_3.Rmd

---
title: "Bayesian data analysis demo 2.3"
author: "Aki Vehtari, Markus Paasiniemi"
date: "`r format(Sys.Date())`"
output:
  html_document:
    theme: readable
    code_download: true
---
## Probability of a girl birth given placenta previa (BDA3 p. 37).

Simulate samples from Beta(438,544), draw a histogram with
quantiles, and do the same for a transformed variable.

ggplot2 is used for plotting, tidyr for manipulating data frames

```{r setup, message=FALSE, error=FALSE, warning=FALSE}
library(ggplot2)
theme_set(theme_minimal())
library(tidyr)
```

Sample from posterior Beta(438,544).
Obtain all draws at once and store them in vector 'theta'

```{r }
a <- 438
b <- 544
theta <- rbeta(10000, a, b)
```

Compute odds ratio for all draws

```{r }
phi <- (1 - theta) / theta
```

Compute 2.5% and 97.5% quantile approximation using samples

```{r }
quantiles <- c(0.025, 0.975)
thetaq <- quantile(theta, quantiles)
phiq <- quantile(phi, quantiles)
```

Histogram plots with 30 bins for theta and phi

```{r }
# merge the data into one data frame for plotting
df1 <- data.frame(phi,theta) %>% pivot_longer(everything())
# merge quantiles into one data frame for plotting
df2 <- data.frame(phi = phiq, theta = thetaq) %>% pivot_longer(everything())
ggplot() +
  geom_histogram(data = df1, aes(value), bins = 30) +
  geom_vline(data = df2, aes(xintercept = value), linetype = 'dotted') +
  facet_wrap(~name, ncol = 1, scales = 'free_x')  +
  labs(x = '', y = '') +
  scale_y_continuous(breaks = NULL)
```