Nothing
BinomGrid <-
expand.grid(pi = seq(0, 1, by = 0.001)) %>%
mutate(
prior = 1, # uniform prior
likelihood = dbinom(20, size = 50, prob = pi),
posterior = prior * likelihood # kernel of posterior
)
posterior_sample <-
with(BinomGrid, sample(pi, size = 1e5, prob = posterior, replace = TRUE))
# credible interval
cdata(~posterior_sample, 0.95) # central 95% credible interval
# compare with analytical result above
gf_dhistogram( ~ posterior_sample, binwidth = 0.02, alpha = 0.4) %>%
gf_dist("beta", shape1 = 21, shape2 = 31, color = "navy")
qbeta(c(0.025, 0.975), shape1 = 21, shape2 = 31)
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