# Matti Vihola: On the scalability of conditional particle filters

**Time: **
Mon 2019-02-11 15.15 - 16.15

**Lecturer: **
Matti Vihola (University of Jyväskylä)

**Location: ** Room F11, Lindstedtsv. 22, KTH

## Abstract

Abstract: Hidden Markov models (HMMs) (also known as state-space models) are a flexible framework for time-series modelling. Full Bayesian inference of non-linear and/or non-Gaussian HMMs has remained a challenge until the recently introduced particle Markov chain Monte Carlo methods (Andrieu, Doucet and Holenstein, J. R. Stat. Soc. Ser. B Stat. Methodol., 2010). In particular, the conditional particle filter (CPF), and its backward sampling variant (CBPF), have been found efficient in many challenging settings.

We discuss the scalability properties of the CPF and the CBPF with respect to the time horizon (length of the time series). Our theoretical results align well with the empirical observations about the efficiency. In particular, our findings about the CBPF confirm the long held view that the CBPF remains an effective sampler with a fixed number of samples even as the time horizon increases. Our analysis of the CBPF relies on analysis of a so-called coupled conditional backward sampling particle filter (CCBPF) algorithm, which is interesting on its own right. Indeed, CCBPF is a simple algorithmic variant of the methods suggested by Jacob, Lindsten and Schön (JASA, to appear) for unbiased estimation with respect to the smoothing distribution of a HMM.