gamma.prior: Gamma prior distribution

In Boom: Bayesian Object Oriented Modeling

Gamma prior distribution

Description

Specifies gamma prior distribution.

Usage

  GammaPrior(a = NULL, b = NULL, prior.mean = NULL, initial.value = NULL)
  TruncatedGammaPrior(a = NULL, b = NULL, prior.mean = NULL,
                      initial.value = NULL,
                      lower.truncation.point = 0,
                      upper.truncation.point = Inf)

Arguments

a	The shape parameter in the Gamma(a, b) distribution.
b	The scale paramter in the Gamma(a, b) distribution.
prior.mean	The mean the Gamma(a, b) distribution, which is a/b.
initial.value	The initial value in the MCMC algorithm of the variable being modeled.
lower.truncation.point	The lower limit of support for the truncated gamma distribution.
upper.truncation.point	The upper limit of support for the truncated gamma distribution.

Details

The mean of the Gamma(a, b) distribution is a/b and the variance is a/b^2. If prior.mean is not NULL, then one of either a or b must be non-NULL as well.

GammaPrior is the conjugate prior for a Poisson mean or an exponential rate. For a Poisson mean a corresponds to a prior sum of observations and b to a prior number of observations. For an exponential rate the roles are reversed a represents a number of observations and b the sum of the observed durations. The gamma distribution is a generally useful for parameters that must be positive.

The gamma distribution is the conjugate prior for the reciprocal of a Guassian variance, but SdPrior should usually be used in that case.

A TruncatedGammaPrior is a GammaPrior with support truncated to the interval (lower.truncation.point, upper.truncation.point).

If an object specifically needs a GammaPrior you typically cannot pass a TruncatedGammaPrior.

Author(s)

Steven L. Scott [e-mail]

References

Gelman, Carlin, Stern, Rubin (2003), "Bayesian Data Analysis", Chapman and Hall.

Boom documentation built on May 29, 2024, 5:08 a.m.