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Scaling limits for the transient phase.

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Scaling limits for the transient phase. / Roberts, G. O.; Christian, O.; Rosenthal, J. S.
In: Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 67, No. 2, 2005, p. 253-268.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Roberts, GO, Christian, O & Rosenthal, JS 2005, 'Scaling limits for the transient phase.', Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 67, no. 2, pp. 253-268. https://doi.org/10.1111/j.1467-9868.2005.00500.x

APA

Roberts, G. O., Christian, O., & Rosenthal, J. S. (2005). Scaling limits for the transient phase. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), 253-268. https://doi.org/10.1111/j.1467-9868.2005.00500.x

Vancouver

Roberts GO, Christian O, Rosenthal JS. Scaling limits for the transient phase. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2005;67(2):253-268. doi: 10.1111/j.1467-9868.2005.00500.x

Author

Roberts, G. O. ; Christian, O. ; Rosenthal, J. S. / Scaling limits for the transient phase. In: Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2005 ; Vol. 67, No. 2. pp. 253-268.

Bibtex

@article{797734cf577b40b8be55516c94aad592,
title = "Scaling limits for the transient phase.",
abstract = "The paper considers high dimensional Metropolis and Langevin algorithms in their initial transient phase. In stationarity, these algorithms are well understood and it is now well known how to scale their proposal distribution variances. For the random-walk Metropolis algorithm, convergence during the transient phase is extremely regular—to the extent that the algo-rithm's sample path actually resembles a deterministic trajectory. In contrast, the Langevin algorithm with variance scaled to be optimal for stationarity performs rather erratically. We give weak convergence results which explain both of these types of behaviour and practical guidance on implementation based on our theory.",
keywords = "Markov chain Monte Carlo methods • Metropolis–Hastings algorithm • Transient phase • Weak convergence",
author = "Roberts, {G. O.} and O. Christian and Rosenthal, {J. S.}",
year = "2005",
doi = "10.1111/j.1467-9868.2005.00500.x",
language = "English",
volume = "67",
pages = "253--268",
journal = "Journal of the Royal Statistical Society: Series B (Statistical Methodology)",
issn = "1369-7412",
publisher = "Wiley-Blackwell",
number = "2",

}

RIS

TY - JOUR

T1 - Scaling limits for the transient phase.

AU - Roberts, G. O.

AU - Christian, O.

AU - Rosenthal, J. S.

PY - 2005

Y1 - 2005

N2 - The paper considers high dimensional Metropolis and Langevin algorithms in their initial transient phase. In stationarity, these algorithms are well understood and it is now well known how to scale their proposal distribution variances. For the random-walk Metropolis algorithm, convergence during the transient phase is extremely regular—to the extent that the algo-rithm's sample path actually resembles a deterministic trajectory. In contrast, the Langevin algorithm with variance scaled to be optimal for stationarity performs rather erratically. We give weak convergence results which explain both of these types of behaviour and practical guidance on implementation based on our theory.

AB - The paper considers high dimensional Metropolis and Langevin algorithms in their initial transient phase. In stationarity, these algorithms are well understood and it is now well known how to scale their proposal distribution variances. For the random-walk Metropolis algorithm, convergence during the transient phase is extremely regular—to the extent that the algo-rithm's sample path actually resembles a deterministic trajectory. In contrast, the Langevin algorithm with variance scaled to be optimal for stationarity performs rather erratically. We give weak convergence results which explain both of these types of behaviour and practical guidance on implementation based on our theory.

KW - Markov chain Monte Carlo methods • Metropolis–Hastings algorithm • Transient phase • Weak convergence

U2 - 10.1111/j.1467-9868.2005.00500.x

DO - 10.1111/j.1467-9868.2005.00500.x

M3 - Journal article

VL - 67

SP - 253

EP - 268

JO - Journal of the Royal Statistical Society: Series B (Statistical Methodology)

JF - Journal of the Royal Statistical Society: Series B (Statistical Methodology)

SN - 1369-7412

IS - 2

ER -