On the evaluation of poly-t density functions
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Abstract Poly- t densities are defined by the property that their kernel is a product, or a ratio of products, of multivariate t -density kernels. As discussed in Dreze (1977), these densities arise as Bayesian posterior densities for regression coefficients under a variety of specifications for the prior density and the data generating process. We have therefore developed methods and computer algorithms to evaluate integrating constants and other characteristics of poly- t densities with no more than a single quadratic form in the numerator (section 2). As a by-product of our analysis we have also derived an algorithm for the computation of moments of positive definite quadratic forms in Normal variables (section 3). In section 4 we discuss inference on the sampling variances associated with the models discussed in Dreze (1977).
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