binpost: Random sampling from a binomial posterior distribution

Description

Samples from the posterior distribution of the probability $p$ of a binomial distribution.

Usage

binpost(n, prior, ds_bin, param = c("logit", "p"))

Arguments

A numeric scalar. The size of posterior sample required.

prior

A function to evaluate the prior, created by set_bin_prior.

ds_bin

A numeric list. Sufficient statistics for inference about a binomial probability $p$. Contains

n_raw : number of raw observations
m : number of threshold exceedances.

param

A character scalar. Only relevant if prior$prior is a (user-supplied) R function. param specifies the parameterization of the posterior distribution that ru uses for sampling.

If param = "p" the original parameterization $p$ is used.

If param = "logit" (the default) then ru samples from the posterior for the logit of $p$, before transforming back to the $p$-scale.

The latter tends to make the optimizations involved in the ratio-of-uniforms algorithm more stable and to increase the probability of acceptance, but at the expense of slower function evaluations.

Value

An object (list) of class "binpost" with components

bin_sim_vals: An n by 1 numeric matrix of values simulated from the posterior for the binomial probability $p$
bin_logf: A function returning the log-posterior for $p$.
bin_logf_args: A list of arguments to bin_logf.

If prior$prior is a (user-supplied) R function then this list also contains ru_object the object of class "ru" returned by ru.

Details

If prior$prior == "bin_beta" then the posterior for $p$ is a beta distribution so rbeta is used to sample from the posterior.

If prior$prior == "bin_mdi" then rejection sampling is used to sample from the posterior with an envelope function equal to the density of a beta(ds$m + 1, ds$n_raw - ds$m + 1) density.

If prior$prior == "bin_northrop" then rejection sampling is used to sample from the posterior with an envelope function equal to the posterior density that results from using a Haldane prior.

If prior$prior is a (user-supplied) R function then ru is used to sample from the posterior using the generalised ratio-of-uniforms method.

Examples

Run this code

# NOT RUN {
data(gom)
u <- quantile(gom, probs = 0.65)
ds_bin <- list()
ds_bin$n_raw <- length(gom)
ds_bin$m <- sum(gom > u)
bp <- set_bin_prior(prior = "jeffreys")
temp <- binpost(n = 1000, prior = bp, ds_bin = ds_bin)
graphics::hist(temp$bin_sim_vals, prob = TRUE)

# Setting a beta prior (Jeffreys in this case) by hand
beta_prior_fn <- function(p, ab) {
  return(stats::dbeta(p, shape1 = ab[1], shape2 = ab[2], log = TRUE))
}
jeffreys <- set_bin_prior(beta_prior_fn, ab = c(1 / 2, 1 / 2))
temp <- binpost(n = 1000, prior = jeffreys, ds_bin = ds_bin)
# }