Description:
<p>Explicit calculus for the posterior distribution of convolution mixtures of weighted gamma processes on Polish spaces are derived. This serves to extend the results of Lo and Weng (1989) to a semiparametric setting on arbitrary spaces. The result of this study is applied to two different types of general semiparametric multiplicative intensity models. One in which a prior is constructed based on q conditionally independent weighted gamma measures given a Euclidean parameter and a second dependent model where different hazard rates are based on a common mixing measure. The latter model seems natural for some types of deconvolution models or regression models. As an example, it is shown how this provides a full (implementable) posterior analysis of the Cox regression model. The results also provide the explicit posterior distribution for the Poisson/Gamma random field model considered by Wolpert and Ickstadt (1998a).</p>