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Stochastic algorithms for Bayesian model selection of AR processes

In this paper we address the problem of determining the dimensions of an autoregressive process in a Bayesian framework under various assumptions, including stationarity of the process. Solving this problem requires the ability to solve integration and/or optimization problems of complicated posterior distributions. We thus propose efficient stochastic algorithms based on Markov chain Monte Carlo methods. Their convergence is established and computer simulations are provided, demonstrating the efficiency of the approach adopted.