An application of MCMC methods for the multiple change-points problem
Signal Processing - Special section on Markov Chain Monte Carlo (MCMC) methods for signal processing
Bayesian covariance matrix estimation using a mixture of decomposable graphical models
Statistics and Computing
Maximum likelihood estimation in nonlinear mixed effects models
Computational Statistics & Data Analysis
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A new methodology for model determination in decomposable graphical Gaussian models (Dawid and Lauritzen in Ann. Stat. 21(3), 1272---1317, 1993) is developed. The Bayesian paradigm is used and, for each given graph, a hyper-inverse Wishart prior distribution on the covariance matrix is considered. This prior distribution depends on hyper-parameters. It is well-known that the models's posterior distribution is sensitive to the specification of these hyper-parameters and no completely satisfactory method is registered. In order to avoid this problem, we suggest adopting an empirical Bayes strategy, that is a strategy for which the values of the hyper-parameters are determined using the data. Typically, the hyper-parameters are fixed to their maximum likelihood estimations. In order to calculate these maximum likelihood estimations, we suggest a Markov chain Monte Carlo version of the Stochastic Approximation EM algorithm. Moreover, we introduce a new sampling scheme in the space of graphs that improves the add and delete proposal of Armstrong et al. (Stat. Comput. 19(3), 303---316, 2009). We illustrate the efficiency of this new scheme on simulated and real datasets.