Construction of a prior distribution for a binomial probability \(p\)

Constructs a prior distribution for use as the argument bin_prior in rpost or in binpost. The user can choose from a list of in-built priors or specify their own prior function, returning the log of the prior density, using an R function and arguments for hyperparameters.

Usage

set_bin_prior(
  prior = c("jeffreys", "laplace", "haldane", "beta", "mdi", "northrop"),
  ...
)

Arguments

prior

Either

• An R function that returns the value of the log of the prior density (see Examples), or

• A character string giving the name of the prior for \(p\). See Details for a list of priors available.

...

Further arguments to be passed to the user-supplied or in-built prior function. For the latter this is only relevant if prior = "beta", when ab can be passed. See Details.

Value

A list of class "binprior". The first component is the name of the input prior. Apart from the MDI prior this will be "beta", in which case the other component of the list is a vector of length two giving the corresponding values of the beta parameters.

Details

Binomial priors. The names of the binomial priors set using bin_prior are:

• "jeffreys": the Jeffreys beta(1/2, 1/2) prior.

• "laplace": the Bayes-Laplace beta(1, 1) prior.

• "haldane": the Haldane beta(0, 0) prior.

• "beta": a beta(\(\alpha, \beta\)) prior. The argument ab is a vector containing c(\(\alpha, \beta\)). The default is ab = c(1, 1).

• "mdi": the MDI prior \(\pi(p) = 1.6186 p^p (1-p)^{1-p}\), for \(0 < p < 1.\)

• "northrop": the improper prior \(\pi(p)=\{-\ln(1-p)\}^{-1}(1-p)^{-1}\), for \(0 < p < 1.\)

Apart from the last two priors these are all beta distributions.

See also

binpost for sampling from a binomial posterior distribution.

Examples

bp <- set_bin_prior(prior = "jeffreys")

# Setting the Jeffreys prior 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))