TY - JOUR

T1 - Stability of sequential Monte Carlo samplers via the Foster-Lyapunov condition

AU - Jasra, Ajay

AU - Doucet, Arnaud

N1 - Generated from Scopus record by KAUST IRTS on 2019-11-20

PY - 2008/12/1

Y1 - 2008/12/1

N2 - Sequential Monte Carlo (SMC) samplers [Del Moral, P., Doucet, A., Jasra, A., 2006. Sequential Monte Carlo samplers. J. Roy. Statist. Soc. B 68, 411-436] are designed to simulate from a sequence of probability measures on a common measurable space (E, E). One way to measure the accuracy of the resulting Monte Carlo estimates is the asymptotic variance in the central limit theorem (CLT). We investigate the conditions, for algorithms used in practice, which are sufficient to ensure that the resulting expression is upper bounded, of which, the typical conditions (e.g. [Chopin, N., 2004. Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Statist. 32, 2385-2411]) are quite restrictive. We use the Foster-Lyapunov condition and contractions in the f-norm of the Markov kernels [Douc, R., Moulines, E., Rosenthal, J.S., 2004. Quantitative bounds on convergence of time-inhomogeneous Markov chains. Ann. Appl. Probab. 14, 1643-1665] to establish quantitative bounds on the asymptotic variance. © 2008 Elsevier B.V. All rights reserved.

AB - Sequential Monte Carlo (SMC) samplers [Del Moral, P., Doucet, A., Jasra, A., 2006. Sequential Monte Carlo samplers. J. Roy. Statist. Soc. B 68, 411-436] are designed to simulate from a sequence of probability measures on a common measurable space (E, E). One way to measure the accuracy of the resulting Monte Carlo estimates is the asymptotic variance in the central limit theorem (CLT). We investigate the conditions, for algorithms used in practice, which are sufficient to ensure that the resulting expression is upper bounded, of which, the typical conditions (e.g. [Chopin, N., 2004. Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. Ann. Statist. 32, 2385-2411]) are quite restrictive. We use the Foster-Lyapunov condition and contractions in the f-norm of the Markov kernels [Douc, R., Moulines, E., Rosenthal, J.S., 2004. Quantitative bounds on convergence of time-inhomogeneous Markov chains. Ann. Appl. Probab. 14, 1643-1665] to establish quantitative bounds on the asymptotic variance. © 2008 Elsevier B.V. All rights reserved.

UR - https://linkinghub.elsevier.com/retrieve/pii/S016771520800268X

UR - http://www.scopus.com/inward/record.url?scp=54049111768&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2008.05.023

DO - 10.1016/j.spl.2008.05.023

M3 - Article

SN - 0167-7152

VL - 78

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 17

ER -