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seminario di statistica matematica
AVVISO DI SEMINARIO
Il giorno 13 ottobre 2005, alle ore 15.00, nell'aula seminari del VI
piano del Dipartimento di Matematica del Politecnico di Milano,
il Prof. Giovanni Petris del Department of Mathematical Sciences,
University of Arkansas, USA, terra' il seminario dal titolo:
"A NEW AUTOMATIC SAMPLER FOR TRANSDIMENSIONAL MARKOV CHAIN MONTE CARLO"
ABSTRACT
Modern applied Bayesian statistics relies heavily on simulation methods
for the analysis of posterior distributions. Algorithms to simulate
from a Markov chain having a prescribed limiting distribution are
nowadays widely available and, for a large class of standard models,
easy to implement. The case of posterior distributions defined on a
space of variable dimension, such as those arising in problems of
variable selection for regression models, is considerably harder. In
fact, although several algorithms to sample from a Markov chain with
such a limiting distribution have been proposed in the literature - most
notably the so-called Reversible Jump -, they are all difficult to
implement on a routine basis and very ill-suited for an automatic use.
In the case of reversible jump, the main drawback is the need to devise
jump proposals in a clever way, so that the sampler moves reasonably
fast between different regions of the support of the posterior. The
calculation of the Jacobians entering the acceptance probabilities may
also be unappealing for a certain class of practitioners. We propose a
new approach to transdimensional Markov chain simulation, based on a
simple geometric idea used to map spaces of different dimension onto a
space having a fixed dimension. This makes it possible to use standard
fixed-dimension samplers also in the transdimensional case. It should be
noted that the map mentioned above can be evaluated in an automatic way
based only on the density of the target distribution in regions of
different dimension. To make the approach even more automatic, we
advocate the use of a multidimensional version of Adaptive Rejection
Metropolis Sampling to simulate from the transformed target density. In
this way the user has only to specify the set of posterior densities on
the different parts of the variable dimensional support. General purpose
functions for implementing the proposed algorithms have been written for
the computer language R.
Tutti gli interessati sono invitati a partecipare.
Alessandra Guglielmi
--
Alessandra Guglielmi
Dipartimento di Matematica
Politecnico di Milano
e-mail: alessandra.guglielmi@mate.polimi.it
pagina web: http://www.mate.polimi.it
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