Reversible Jump Markov Chain Monte Carlo Strategies for Bayesian Model Selection in Autoregressive Processes

Abstract.  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.

[1]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[2]  H. Akaike.  A new look at the statistical model identification , 1974 .

[3]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[4]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[5]  B. Friedlander,et al.  Lattice filters for adaptive processing , 1982, Proceedings of the IEEE.

[6]  Donald Poskitt,et al.  On the posterior odds of time series models , 1983 .

[7]  Fredrik Gustafsson,et al.  Twenty-one ML estimators for model selection , 1995, Autom..

[8]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[9]  R. Kohn,et al.  Bayesian Estimation of an Autoregressive Model Using MarkovChain , 1996 .

[10]  R. Kohn,et al.  Bayesian estimation of an autoregressive model using Markov chain Monte Carlo , 1996 .

[11]  P. Green,et al.  Corrigendum: On Bayesian analysis of mixtures with an unknown number of components , 1997 .

[12]  P. Green,et al.  On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion) , 1997 .

[13]  Michael A. West,et al.  Bayesian Forecasting and Dynamic Models (2nd edn) , 1997, J. Oper. Res. Soc..

[14]  Simon J. Godsill,et al.  On the relationship between MCMC model uncertainty methods , 1997 .

[15]  F P Wheeler,et al.  Bayesian Forecasting and Dynamic Models (2nd edn) , 1998, J. Oper. Res. Soc..

[16]  Robert Kohn,et al.  Additive nonparametric regression with autocorrelated errors , 1998 .

[17]  Simon J. Godsill,et al.  A reversible jump sampler for autoregressive time series , 1997, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[18]  Christian P. Robert,et al.  Bayesian Inference in Hidden Markov Models through Jump Markov Chain Monte Carlo , 1999 .

[19]  Matthew West,et al.  Priors and component structures in autoregressive time series models , 1999 .

[20]  M. West,et al.  Bayesian Inference on Periodicities and Component Spectral Structure in Time Series , 1999 .

[21]  C. Robert,et al.  Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method , 2000 .

[22]  Hoon Kim,et al.  Monte Carlo Statistical Methods , 2000, Technometrics.

[23]  Simon J. Godsill,et al.  Bayesian model selection of autoregressive processes , 2000 .

[24]  S. Godsill.  On the Relationship Between Markov chain Monte Carlo Methods for Model Uncertainty , 2001 .

[25]  Arto Luoma,et al.  Bayesian Model Selection , 2016 .