When to use: When we want to find the posterior probability mass given a specific boundary – or set of boundaries.

• Example: What is the posterior probability that the proportion of water (p) is < 0.5?

• Calculate using samples from the posterior:

• draw our 10,000 sample from our posterior distribution, w/ replacement

• Samples <- sample(p_grid, prob=posterior, size=1e4, replacement=TRUE)

• add up the samples < 0.5

• Sum(samples < 0.5) / 1e4

• 0.1726