Trans-dimensional Bayesian non-parametrics with spatial point processes

Point processes are a class of models where the notion of variable dimension is inherent. The main part of this discussion is concerned with the application of marked point processes as prior models in nonparametric Bayesian function estimation, reformulating and revising earlier joint work with Elja Arjas and listing some other related work (Section 2). Accordingly, the discussion is centered on trans-dimensional modelling rather than on the simulation techniques themselves, and connects to some of the material in the chapters by Sylvia Richardson and Hurn, Husby and Rue. I shall end, however, with an example illustrating the role of the dimension-matching requirement (Section 3). The point made there is rather marginal to Green’s main message, but hopefully interesting and/or instructive to modellers working with constraints.