Draw from the posterior of a binomial proportion

Draws from the Jeffreys posterior Beta(x + 1/2, n - x + 1/2) implied by observing estimate * n_replicates successes in n_replicates replicates.

This replaces approximating an exact binomial interval by a symmetric normal and discarding the draws that fall outside (0, 1). The posterior is supported on (0, 1) by construction, so no draw is ever discarded, and it retains the skewness that the normal approximation removes – which matters most for the small type I errors these comparisons are made at.

Usage

sample_binomial_proportion(n_samples, estimate, n_replicates)

Arguments

n_samples

Number of draws to return.

estimate

The estimated proportion.

n_replicates

The number of replicates the estimate is based on.

Value

A numeric vector of n_samples draws in (0, 1).