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BAYESIAN DETECTION AND ANALYSIS OF CHANGING TRANSITION MATRICES OF STATIONARY MARKOV CHAINS
Author(s) -
Groenewald P.C.N.,
Schoeman A.C.
Publication year - 2004
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2004.00353.x
Subject(s) - markov chain , mathematics , markov chain monte carlo , stochastic matrix , bayesian probability , prior probability , markov chain mixing time , bayes' theorem , continuous time markov chain , upper and lower bounds , bayes factor , variable order markov model , markov model , statistical physics , statistics , mathematical analysis , physics
Summary This paper considers the detection of abrupt changes in the transition matrix of a Markov chain from a Bayesian viewpoint. It derives Bayes factors and posterior probabilities for unknown numbers of change‐points, as well as the positions of the change‐points, assuming non‐informative but proper priors on the parameters and fixed upper bound. The Markov chain Monte Carlo approach proposed by Chib in 1998 for estimating multiple change‐points models is adapted for the Markov chain model. It is especially useful when there are many possible change‐points. The method can be applied in a wide variety of disciplines and is particularly relevant in the social and behavioural sciences, for analysing the effects of events on the attitudes of people.