Gamma prior distribution
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)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. |
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.
Steven L. Scott steve.the.bayesian@gmail.com
Gelman, Carlin, Stern, Rubin (2003), "Bayesian Data Analysis", Chapman and Hall.
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