A little animation of Bayesian updating with a

bayesian_updating.R

library(dplyr)
library(tidyr)
library(stringr)
library(ggplot2)
library(gganimate)

#make those samples!
set.seed(3003)
samps <- replicate(9, rbinom(1,1,prob = 0.3))
running_samps <- cumsum(samps)

#make those posteriors for each trial!
posterior_tibble <- tibble(
  h = seq(0, 1, length.out = 100),
) %>%
  crossing(tibble(trial = 0:9, samp = c(1, running_samps) )) %>%
  
  #get running likelihood * prior
  group_by(h) %>%
  arrange(trial) %>%
  mutate(lik = dbinom(running_samps, prob = h[1], size = trial)) %>%
  mutate(posterior = cumprod(lik)) %>%
  
  #now throw in the p(d) denominator for each trial
  group_by(trial) %>%
  mutate(posterior = posterior/sum(posterior)) %>%
  ungroup() %>%
  
  #make the titles nicer
  mutate(trial = str_c("trial ", trial),
         trial = str_replace(trial, "trial 0", "prior"))

#plot with facets
ggplot(posterior_tibble,
       aes(x = h, y = posterior)) +
  geom_line() +
  facet_wrap(~trial)

#plot with animation
ggplot(posterior_tibble,
       aes(x = h, y = posterior)) +
  geom_line(size = 1.2) +
  labs(title = '{closest_state}', 
       y = "probability",
       x = "fraction white") +
  transition_states(trial ,
                    transition_length = 2,
                    state_length = 3)