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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 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

Volume

51

Issue

2

Pages

437-463

Publisher

Institute of Mathematical Statistics

Version

  • AM (Accepted Manuscript)

Rights holder

© Institute of Mathematical Statistics

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

Publication date

2023-04-01

Copyright date

2023

ISSN

0090-5364

Language

  • en

Depositor

Dr Axel Finke. Deposit date: 19 January 2023

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