Convergence controls for MCMC algorithms, with applications to hidden Markov chains. (English) Zbl 0968.62049
Summary: In complex models like hidden Markov chains, the convergence of the MCMC algorithms used to approximate the posterior distribution and the Bayes estimates of the parameters of interest must be controlled in a robust manner. We propose in this paper a series of online controls, which rely on classical nonparametric tests, to evaluate independence from the start-up distribution, stability of the Markov chain, and asymptotic normality. These tests lead to graphical control spreadsheets which are presented in the set-up of normal mixture hidden Markov chains to compare the full Gibbs sampler with an aggregated Gibbs sampler based on the forward-backward formulas.
MSC:
| 62G10 | Nonparametric hypothesis testing |
| 65C40 | Numerical analysis or methods applied to Markov chains |
Keywords:
allocation; backward formula; Kolmogorov-Smirnov tests; mixture model; normality test; Spearman independence test; stationary; subsamplingReferences:
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