Geodesic
Local degeneracy of Markov chain Monte Carlo methods
ESAIM: Probability and Statistics, Tome 18 (2014), pp. 713-725

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We study asymptotic behavior of Markov chain Monte Carlo (MCMC) procedures. Sometimes the performances of MCMC procedures are poor and there are great importance for the study of such behavior. In this paper we call degeneracy for a particular type of poor performances. We show some equivalent conditions for degeneracy. As an application, we consider the cumulative probit model. It is well known that the natural data augmentation (DA) procedure does not work well for this model and the so-called parameter-expanded data augmentation (PX-DA) procedure is considered to be a remedy for it. In the sense of degeneracy, the PX-DA procedure is better than the DA procedure. However, when the number of categories is large, both procedures are degenerate and so the PX-DA procedure may not provide good estimate for the posterior distribution.

DOI : 10.1051/ps/2014004
Classification : 65C40, 62E20
Keywords: Markov chain Monte Carlo, asymptotic normality, cumulative link model 
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     author = {Kamatani, Kengo},
     title = {Local degeneracy of {Markov} chain {Monte} {Carlo} methods},
     journal = {ESAIM: Probability and Statistics},
     pages = {713--725},
     publisher = {EDP-Sciences},
     volume = {18},
     year = {2014},
     doi = {10.1051/ps/2014004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2014004/}
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Kamatani, Kengo. Local degeneracy of Markov chain Monte Carlo methods. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 713-725. doi: 10.1051/ps/2014004

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