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Conditional sequential Monte Carlo in high dimensions

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journal contribution
posted on 2023-01-20, 10:55 authored by Axel FinkeAxel Finke, Alexandre H Thiery

The iterated conditional sequential Monte Carlo (i-CSMC) algorithm from Andrieu, Doucet and Holenstein (2010) is an MCMC approach for efficiently sampling from the joint posterior distribution of the T latent states in challenging time-series models, e.g. in non-linear or non-Gaussian statespace models. It is also the main ingredient in particle Gibbs samplers which infer unknown model parameters alongside the latent states. In this work, we first prove that the i-CSMC algorithm suffers from a curse of dimension in the dimension of the states, D: it breaks down unless the number of samples (‘particles’), N, proposed by the algorithm grows exponentially with D.

Then, we present a novel ‘local’ version of the algorithm which proposes particles using Gaussian random-walk moves that are suitably scaled with D. We prove that this iterated random-walk conditional sequential Monte Carlo (i-RW-CSMC) algorithm avoids the curse of dimension: for arbitrary N, its acceptance rates and expected squared jumping distance converge to non-trivial limits as D→∞. If T = N = 1, our proposed algorithm reduces to a Metropolis–Hastings or Barker’s algorithm with Gaussian random-walk moves and we recover the well known scaling limits for such algorithms.

Funding

Singapore Ministry of Education Tier 2 (MOE2016-T2-2-135)

Young Investigator Award Grant (NUSYIA FY16 P16; R-155-000-180-133)

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Annals of Statistics

Publisher

Institute of Mathematical Statistics

Version

AM (Accepted Manuscript)

Publisher statement

This paper was accepted for publication in Annals of Statistics. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (https://creativecommons.org/licenses/by-nc-nd/4.0/).

Acceptance date

2022-12-14

ISSN

0090-5364

Language

en

Depositor

Dr Axel Finke. Deposit date: 19 January 2023