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A geometric approach to transdimensional markov chain monte carlo
Author(s) -
Petris Giovanni,
Tardella Luca
Publication year - 2003
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315857
Subject(s) - markov chain monte carlo , markov chain , monte carlo method , linear subspace , computer science , markov chain mixing time , subspace topology , statistical physics , hybrid monte carlo , dimension (graph theory) , mathematical optimization , mathematics , markov model , algorithm , variable order markov model , artificial intelligence , combinatorics , statistics , machine learning , pure mathematics , physics
Abstract The authors present theoretical results that show how one can simulate a mixture distribution whose components live in subspaces of different dimension by reformulating the problem in such a way that observations may be drawn from an auxiliary continuous distribution on the largest subspace and then transformed in an appropriate fashion. Motivated by the importance of enlarging the set of available Markov chain Monte Carlo (MCMC) techniques, the authors show how their results can be fruitfully employed in problems such as model selection (or averaging) of nested models, or regeneration of Markov chains for evaluating standard deviations of estimated expectations derived from MCMC simulations.