Rates of convergence for everywhere-positive Markov chains

J. R. Baxter; Jeffrey S. Rosenthal

doi:10.1016/0167-7152(94)00085-M

Rates of convergence for everywhere-positive Markov chains

J. R. Baxter, Jeffrey S. Rosenthal

School of Mathematics

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

We generalize and simplify a result of Schervish and Carlin (1992) concerning the convergence of Markov chains to their stationary distributions. We prove geometric convergence for any Markov chain whose transition operator is compact and has everywhere-positive density functions (with respect to some reference measure). We also provide, without requiring compactness, a quantitative estimate of the convergence rate, given in terms of the stationary distribution.

Original language	English (US)
Pages (from-to)	333-338
Number of pages	6
Journal	Statistics and Probability Letters
Volume	22
Issue number	4
DOIs	https://doi.org/10.1016/0167-7152(94)00085-M
State	Published - Mar 1995

Bibliographical note

Funding Information:
We thank Peter gosenthal for helpful discussions, and thank the referee for useful comments. This work was partially supported by NSF and by NSERC.

Keywords

Compact operator
Geometric convergence
Gibbs sampler
Hilbert-Schmidt condition
Markov chain
Monte Carlo
Stationary distribution

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10.1016/0167-7152(94)00085-M

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title = "Rates of convergence for everywhere-positive Markov chains",

abstract = "We generalize and simplify a result of Schervish and Carlin (1992) concerning the convergence of Markov chains to their stationary distributions. We prove geometric convergence for any Markov chain whose transition operator is compact and has everywhere-positive density functions (with respect to some reference measure). We also provide, without requiring compactness, a quantitative estimate of the convergence rate, given in terms of the stationary distribution.",

keywords = "Compact operator, Geometric convergence, Gibbs sampler, Hilbert-Schmidt condition, Markov chain, Monte Carlo, Stationary distribution",

author = "Baxter, \{J. R.\} and Rosenthal, \{Jeffrey S.\}",

note = "Funding Information: We thank Peter gosenthal for helpful discussions, and thank the referee for useful comments. This work was partially supported by NSF and by NSERC.",

year = "1995",

month = mar,

doi = "10.1016/0167-7152(94)00085-M",

language = "English (US)",

volume = "22",

pages = "333--338",

journal = "Statistics and Probability Letters",

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TY - JOUR

T1 - Rates of convergence for everywhere-positive Markov chains

AU - Baxter, J. R.

AU - Rosenthal, Jeffrey S.

N1 - Funding Information: We thank Peter gosenthal for helpful discussions, and thank the referee for useful comments. This work was partially supported by NSF and by NSERC.

PY - 1995/3

Y1 - 1995/3

N2 - We generalize and simplify a result of Schervish and Carlin (1992) concerning the convergence of Markov chains to their stationary distributions. We prove geometric convergence for any Markov chain whose transition operator is compact and has everywhere-positive density functions (with respect to some reference measure). We also provide, without requiring compactness, a quantitative estimate of the convergence rate, given in terms of the stationary distribution.

AB - We generalize and simplify a result of Schervish and Carlin (1992) concerning the convergence of Markov chains to their stationary distributions. We prove geometric convergence for any Markov chain whose transition operator is compact and has everywhere-positive density functions (with respect to some reference measure). We also provide, without requiring compactness, a quantitative estimate of the convergence rate, given in terms of the stationary distribution.

KW - Compact operator

KW - Geometric convergence

KW - Gibbs sampler

KW - Hilbert-Schmidt condition

KW - Markov chain

KW - Monte Carlo

KW - Stationary distribution

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U2 - 10.1016/0167-7152(94)00085-M

DO - 10.1016/0167-7152(94)00085-M

M3 - Article

AN - SCOPUS:0000178531

SN - 0167-7152

VL - 22

SP - 333

EP - 338

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 4

ER -

Rates of convergence for everywhere-positive Markov chains

Abstract

Bibliographical note

Keywords

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