Stores the prior distributions to be used for Bayesian variable selection
in normal regression models.
This class can be used to specify the prior on non-zero regression coefficients,
the model indicator or the nuisance parameters.
Prior dispersion parameter for covariates undergoing selection
tau.adj
Prior variance in Normal prior for covariates not undergoing selection
r
MOM prior parameter is 2*r
p
Prior inclusion probability for binomial prior on model space
alpha.p
Beta-binomial prior on model space has parameters alpha.p, beta.p
beta.p
Beta-binomial prior on model space has parameters alpha.p, beta.p
alpha
Inverse gamma prior has parameters alpha/2, lambda/2
lambda
Inverse gamma prior has parameters alpha/2, lambda/2
Objects from the Class
Objects can be created by calls of the form new("msPriorSpec",
...), but it is easier to use creator functions.
For priors on regression coefficients use momprior,
imomprior or emomprior.
For prior on model space modelunifprior, modelbinomprior
or modelbbprior.
For prior on residual variance use igprior.
Slots
priorType:
Object of class "character". "coefficients" indicates
that the prior is for the non-zero regression coefficients.
"modelIndicator" that it is for the model indicator,
and "nuisancePars" that it is for the nuisance parameteres.
Several prior distributions are available for each choice of priorType,
and these can be speicified in the slot priorDist.
priorDistr:
Object of class "character".
If priorType=="coefficients", priorDistr can be equal to
"pMOM", "piMOM", "peMOM" or "zellner"
(product moment, product inverse moment, product exponential moment or Zellner prior, respectively).
If priorType=="modelIndicator", priorDistr can be equal to "uniform" or "binomial"
to specify a uniform prior (all models equaly likely a priori) or a binomial prior. For a binomial prior,
the prior inclusion probability for any single variable must be
specified in slot priorPars['p']. For a beta-binomial prior, the
Beta hyper-prior parameters must be in priorPars['alpha.p'] and priorPars['beta.p'].
If priorType=="nuisancePars", priorDistr must be equal to "invgamma". This corresponds to an
inverse gamma distribution for the residual variance, with parameters
specified in the slot priorPars.
priorPars:
Object of class "vector", where each element must be named.
For priorDistr=='pMOM', there must be an element "r" (MOM power
is 2r).
For any priorDistr there must be either an element "tau" indicating
the prior dispersion or elements "a.tau" and "b.tau" specifying an
inverse gamma hyper-prior for "tau".
Optionally, there may be an element "tau.adj" indicating the prior
dispersion for the adjustment variables (i.e. not undergoing variable
selection). If not defined, "tau.adj" is set to 0.001 by default.
For priorDistr=='binomial', there must be either an element "p" specifying the prior inclusion probability
for any single covariate, or a vector with elements "alpha.p" and
"beta.p" specifying a Beta(alpha.p,beta.p) hyper-prior on p.
For priorDistr=='invgamma' there must be elements "alpha" and "lambda". The prior for the residual variance
is an inverse gamma with parameteres .5*alpha and .5*lambda.
Methods
No methods defined with class "msPriorSpec" in the signature.
Note
When new instances of the class are created a series of check are performed to ensure that a valid prior
specification is produced.
Author(s)
David Rossell
References
Johnson VE, Rossell D. Non-Local Prior Densities for Default Bayesian Hypothesis Tests. Journal of the Royal Statistical Society B, 2010, 72, 143-170
Johnson VE, Rossell D. Bayesian model selection in high-dimensional
settings. Journal of the American Statistical Association, 107, 498:649-660.
See Also
See also modelSelection for an example of defining an instance of the class
and perform Bayesian model selection.