A1 Journal article (refereed)
Conditional particle filters with diffuse initial distributions (2021)

Karppinen, S., & Vihola, M. (2021). Conditional particle filters with diffuse initial distributions. Statistics and Computing, 31(3), Article 24. https://doi.org/10.1007/s11222-020-09975-1

JYU authors or editors

Publication details

All authors or editors: Karppinen, Santeri; Vihola, Matti

ISBN: 0960-3174

Journal or series: Statistics and Computing

ISSN: 0960-3174

eISSN: 1573-1375

Publication year: 2021

Volume: 31

Issue number: 3

Article number: 24

Publisher: Springer

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1007/s11222-020-09975-1

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/74498

Abstract

Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov transitions that are reversible with respect to the initial distribution, which can be improper. We focus in particular on random walk type transitions which are reversible with respect to a uniform initial distribution (on some domain), and autoregressive kernels for Gaussian initial distributions. We propose to use online adaptations within the methods. In the case of random walk transition, our adaptations use the estimated covariance and acceptance rate adaptation, and we detail their theoretical validity. We tested our methods with a linear Gaussian random walk model, a stochastic volatility model, and a stochastic epidemic compartment model with time-varying transmission rate. The experimental findings demonstrate that our method works reliably with little user specification and can be substantially better mixing than a direct particle Gibbs algorithm that treats initial states as parameters.

Keywords: Bayesian analysis; Markov chains; mathematical methods; statistics (discipline)

Free keywords: Adaptive Markov chain Monte Carlo; bayesian inference; compartment model; conditional particle filter; diffuse initialisation; Hidden Markov model; smoothing; state space model

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Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 2