2.5 Posterior simulation

We can also validate the posterior model derived using the Bayes’ Rule via simulation.

Start off with specifying the prior and the likelihoods.

prior <- list(fake = 0.4, real = 0.6)
likelihood <- list(fake = 0.2667, real = 0.0222)

We then simulate 10,000 articles as either “real” or “fake” based on the prior probabilities.

set.seed(84735)
articles <- sample_n(tibble(type = c("fake", "real")), size = 10000, 
                     weight = prior, replace = TRUE)

Summary of simulated articles
type	n	percent
fake	4031	40.3%
real	5969	59.7%
Total	10000	100.0%

Against these simulated we add an attribute - “does it have an exclamation (!) mark” based on the likelihoods.

articles <- articles |>
  mutate(data_model = if_else(type == "fake", likelihood$fake, 
                              likelihood$real)) |> 
  rowwise() |>
  mutate(has_exclam = sample(c(T, F), 1, prob = c(data_model, 1-data_model)))

Finally, we filter for those articles which have an exclamation mark and compute the probabilitiy of them being “fake” or “real”. This gives us the posterior probability (simulated).

posterior_prob_sim <- 
  articles |> 
  filter(has_exclam) |> 
  tabyl(type) |> 
  adorn_pct_formatting(digits = 1) |> 
  pull(percent) 

	Fake	Real
prior	40.0%	60.0%
likelihood	26.7%	2.2%
posterior	88.9%	11.1%
posterior (simulated)	89.0%	11.0%