# Local degeneracy of Markov chain Monte Carlo methods

ESAIM: Probability and Statistics (2014)

- Volume: 18, page 713-725
- ISSN: 1292-8100

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topKamatani, Kengo. "Local degeneracy of Markov chain Monte Carlo methods." ESAIM: Probability and Statistics 18 (2014): 713-725. <http://eudml.org/doc/274378>.

@article{Kamatani2014,

abstract = {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.},

author = {Kamatani, Kengo},

journal = {ESAIM: Probability and Statistics},

keywords = {Markov chain Monte Carlo; asymptotic normality; cumulative link model; numerical examples},

language = {eng},

pages = {713-725},

publisher = {EDP-Sciences},

title = {Local degeneracy of Markov chain Monte Carlo methods},

url = {http://eudml.org/doc/274378},

volume = {18},

year = {2014},

}

TY - JOUR

AU - Kamatani, Kengo

TI - Local degeneracy of Markov chain Monte Carlo methods

JO - ESAIM: Probability and Statistics

PY - 2014

PB - EDP-Sciences

VL - 18

SP - 713

EP - 725

AB - 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.

LA - eng

KW - Markov chain Monte Carlo; asymptotic normality; cumulative link model; numerical examples

UR - http://eudml.org/doc/274378

ER -

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