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Reversible Jump Markov Chain Monte Carlo Strategies for Bayesian Model Selection in Autoregressive Processes
Author(s) -
Vermaak J.,
Andrieu C.,
Doucet A.,
Godsill S. J.
Publication year - 2004
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2004.00380.x
Subject(s) - markov chain monte carlo , reversible jump markov chain monte carlo , autoregressive model , posterior probability , bayesian inference , mathematics , model selection , bayesian probability , jump , monte carlo method , algorithm , computer science , econometrics , statistics , physics , quantum mechanics
. This paper addresses the problem of Bayesian inference in autoregressive (AR) processes in the case where the correct model order is unknown. Original hierarchical prior models that allow the stationarity of the model to be enforced are proposed. Obtaining the quantities of interest, such as parameter estimates, predictions of future values of the time series, posterior model‐order probabilities, etc., requires integration with respect to the full posterior distribution, an operation which is analytically intractable. Reversible jump Markov chain Monte Carlo (MCMC) algorithms are developed to perform the required integration implicitly by simulating from the posterior distribution. The methods developed are evaluated in simulation studies on a number of synthetic and real data sets.