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Abstract:
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A parameter selection prior is a mixture of discrete and continuous components which allows some or all of the parameters in a statistical model to be exactly zero. Two examples of such priors are a variable selection prior in a Gaussian linear regression model and a covariance selection prior, where the off-diagonal elements of the inverse of the covariance matrix are allowed to be exactly zero. Our article makes the following contributions. First, it sets out a general framework for parameter selection priors; second, it presents a simulation method for estimating normalizing constants for parameter selection priors; third, it applies the methodology to obtain a general class of covariance selection priors; and fourth, it provides an extensive empirical check on the simulation methodology for obtaining the normalizing constants for covariance selection priors.
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