for twitter. showing how to combine a prior (past election results) and data (polls) for certain poll subgroups

bayes update young voters.R

library(tidyverse)

bayes_update_normal = function(
    data_mu,
    data_se,
    prior_mu = 0,
    prior_se = 3){
  
  if(all(data_mu == 0)){
    return(c(0,0))
  }
  
  # calc precision
  data_pre = 1/(data_se^2)
  prior_pre = 1/(prior_se^2)
  
  # new mu
  post_mu = 
    ( (prior_pre / (prior_pre + data_pre)) * prior_mu ) +
    ( (data_pre / (prior_pre + data_pre)) * data_mu ) 
  
  # new variance (then sd)
  post_var = ( ((data_se^2)/1) * prior_se^2 )  /
    (prior_se^2 + ((data_se^2)/1))
  
  post_se = sqrt(post_var)
  
  list(post_mu,post_se)  
}


prior = rnorm(200000, 24, 5)
data = rnorm(200000, 4, 10)
post = bayes_update_normal(mean(data), sd(data), mean(prior), sd(prior))
post = rnorm(200000, post[[1]], post[[2]])

chart = tibble(prior = prior,
       data = data,
       post = post)


ggplot(chart) + 
  geom_vline(xintercept = 0, col = 'gray60') +
  geom_density(aes(x=prior, col = '1. Past vote (24 +/- 5)')) +
  geom_density(aes(x=data, col = '2. Polls (+4 +/- 10)')) +
  geom_density(aes(x=post, col = '3. Posterior')) +
  theme_minimal() +
  labs(x = "Democratic presidential vote margin",
       y = '',
       subtitle = 'Scenario: Very tight prior, low trust in polls',
       col = '',
       title = 'Updating a prior for young voters with polls') +
  theme(axis.title.y = element_blank(),
        axis.ticks.y = element_blank(),
        axis.text.y = element_blank(),
        panel.grid.minor = element_blank(),
        legend.position = 'top') +
  coord_cartesian(xlim=c(-50,50))


mean(post)
sd(post)