Drift, Minorization, and Hitting Times

Research output: Working paper › Preprint › Research

Standard

Drift, Minorization, and Hitting Times. / Anderson, Robert M.; Duanmu, Haosui; Smith, Aaron; Yang, Jun.

arXiv preprint, 2019.

Research output: Working paper › Preprint › Research

Harvard

Anderson, RM, Duanmu, H, Smith, A & Yang, J 2019 'Drift, Minorization, and Hitting Times' arXiv preprint.

APA

Anderson, R. M., Duanmu, H., Smith, A., & Yang, J. (2019). Drift, Minorization, and Hitting Times. arXiv preprint.

Vancouver

Anderson RM, Duanmu H, Smith A, Yang J. Drift, Minorization, and Hitting Times. arXiv preprint. 2019 Oct 14.

Author

Anderson, Robert M. ; Duanmu, Haosui ; Smith, Aaron ; Yang, Jun. / Drift, Minorization, and Hitting Times. arXiv preprint, 2019.

Bibtex

@techreport{cafef24976e843488ed9eca34dbd04cb,
title = "Drift, Minorization, and Hitting Times",
abstract = "The {"}drift-and-minorization{"} method, introduced and popularized in (Rosenthal, 1995; Meyn and Tweedie, 1994; Meyn and Tweedie, 2012), remains the most popular approach for bounding the convergence rates of Markov chains used in statistical computation. This approach requires estimates of two quantities: the rate at which a single copy of the Markov chain {"}drifts{"} towards a fixed {"}small set{"}, and a {"}minorization condition{"} which gives the worst-case time for two Markov chains started within the small set to couple with moderately large probability. In this paper, we build on (Oliveira, 2012; Peres and Sousi, 2015) and our work (Anderson, Duanmu, Smith, 2019a; Anderson, Duanmu, Smith, 2019b) to replace the {"}minorization condition{"} with an alternative {"}hitting condition{"} that is stated in terms of only one Markov chain, and illustrate how this can be used to obtain similar bounds that can be easier to use.",
keywords = "math.PR, math.ST, stat.CO, stat.TH",
author = "Anderson, {Robert M.} and Haosui Duanmu and Aaron Smith and Jun Yang",
note = "18 pages",
year = "2019",
month = oct,
day = "14",
language = "English",
publisher = "arXiv preprint",
type = "WorkingPaper",
institution = "arXiv preprint",

}

RIS

TY - UNPB

T1 - Drift, Minorization, and Hitting Times

AU - Anderson, Robert M.

AU - Duanmu, Haosui

AU - Smith, Aaron

AU - Yang, Jun

N1 - 18 pages

PY - 2019/10/14

Y1 - 2019/10/14

N2 - The "drift-and-minorization" method, introduced and popularized in (Rosenthal, 1995; Meyn and Tweedie, 1994; Meyn and Tweedie, 2012), remains the most popular approach for bounding the convergence rates of Markov chains used in statistical computation. This approach requires estimates of two quantities: the rate at which a single copy of the Markov chain "drifts" towards a fixed "small set", and a "minorization condition" which gives the worst-case time for two Markov chains started within the small set to couple with moderately large probability. In this paper, we build on (Oliveira, 2012; Peres and Sousi, 2015) and our work (Anderson, Duanmu, Smith, 2019a; Anderson, Duanmu, Smith, 2019b) to replace the "minorization condition" with an alternative "hitting condition" that is stated in terms of only one Markov chain, and illustrate how this can be used to obtain similar bounds that can be easier to use.

AB - The "drift-and-minorization" method, introduced and popularized in (Rosenthal, 1995; Meyn and Tweedie, 1994; Meyn and Tweedie, 2012), remains the most popular approach for bounding the convergence rates of Markov chains used in statistical computation. This approach requires estimates of two quantities: the rate at which a single copy of the Markov chain "drifts" towards a fixed "small set", and a "minorization condition" which gives the worst-case time for two Markov chains started within the small set to couple with moderately large probability. In this paper, we build on (Oliveira, 2012; Peres and Sousi, 2015) and our work (Anderson, Duanmu, Smith, 2019a; Anderson, Duanmu, Smith, 2019b) to replace the "minorization condition" with an alternative "hitting condition" that is stated in terms of only one Markov chain, and illustrate how this can be used to obtain similar bounds that can be easier to use.

KW - math.PR

KW - math.ST

KW - stat.CO

KW - stat.TH

M3 - Preprint

BT - Drift, Minorization, and Hitting Times

PB - arXiv preprint

ER -

ID: 361432335