Dear All,

This is to announce a seminar by Peter Green at the Department of
Statistics, Trinity College Dublin on 1 December 1998, 2 o'clock in the
Statistics Building.

Title is

"Perfect simulation, and its possibilities in Bayesian statistics."

All are welcome. Abstract is below. 


With the ultimate objective of Bayesian MCMC with guaranteed convergence,
the purpose of this talk is to describe recent efforts to construct exact
sampling methods for continuous-state Markov chains. We review existing
methods based on gamma-coupling and rejection sampling (Murdoch and Green,
{\it Scandinavian Journal of Statistics}, 1998), that are quite
straightforward to understand, but require a closed form for the transition
kernel and entail cumbersome algebraic manipulation. We then introduce a
new method based on random walk Metropolis, that offer the prospect of more
automatic use, not least because the difficult, continuous, part of the
transition mechanism can be coupled in a generic way, using a proposal
distribution of convenience.

This method is based on a neat decomposition of any unimodal (multivariate)
symmetric density into pieces that may be re-assembled to construct any
translated copy of itself: this allows coupling of a continuum of
Metropolis proposals to a finite set, at least for a compact state space.
We discuss methods for economically coupling the subsequent accept/reject
decisions.

We look towards the possibility that application of such methods could
become sufficiently convenient that they could become the basis for routine
Bayesian computation in the foreseeable future. 

This is joint work with Duncan Murdoch.






__________________________________
Bart Mertens
Department of Statistics
Trinity College Dublin
Dublin 2
Ireland

email: [log in to unmask]
WWW: http://www2.tcd.ie/statistics

Tel. 608-1760 
Fax. 661-5046

International telephone code: (00)-353-1-
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