Transdimensional Markov Chain Monte Carlo Using Hyperplane Inflation in Locally Nested Spaces - Rapporto tecnico n.2-2006 - Dipartimento di Statistica, Probabilità e Statistiche Applicate - Sapienza Università di Roma

We present some new results that extend the geometric approach to trans- dimensional Markov chain Monte Carlo simulations originally proposed in Petris and Tardella (2003). These provide a black-box method to generate a sample from a Markov chain with a prescribed stationary distribution on a disjoint union of Euclidean spaces not necessarily of the same dimension. The only requirement is that the support spaces of different dimensions have to be locally nested and the corresponding densities of the target distribu- tion have to be known up to a normalizing constant. Empirical evidence of effectiveness of the proposed method is provided by a controlled experiment of variable selection in a general regression context as well as by an original approach to mixture of normal models. Rapporto Tecnico #4, Dipartimento di Satistica, Probabilità e Statistiche Applicate, Università "La Sapienza" - Rom