Specifies gamma prior distribution.
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)
The shape parameter in the Gamma(a, b) distribution.
The scale paramter in the Gamma(a, b) distribution.
The mean the Gamma(a, b) distribution, which is a/b.
The initial value in the MCMC algorithm of the variable being modeled.
The lower limit of support for the truncated gamma distribution.
The upper limit of support for the truncated gamma distribution.
Steven L. Scott steve.the.bayesian@gmail.com
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.
Gelman, Carlin, Stern, Rubin (2003), "Bayesian Data Analysis", Chapman and Hall.