Nested particle filters for online parameter estimation in discrete-time state-space Markov models

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Title: Nested particle filters for online parameter estimation in discrete-time state-space Markov models
Authors: Crisan, DO
Miguez, J
Item Type: Journal Article
Abstract: We address the problem of approximating the posterior probability distribution of the fixed parameters of a state-space dynamical system using a sequential Monte Carlo method. The proposed approach relies on a nested structure that employs two layers of particle filters to approximate the posterior probability measure of the static parameters and the dynamic state variables of the system of interest, in a vein similar to the recent “sequential Monte Carlo square” (SMC 2 ) algorithm. However, unlike the SMC 2 scheme, the proposed technique operates in a purely recursive manner. In particular, the computational complexity of the recursive steps of the method introduced herein is constant over time. We analyse the approximation of integrals of real bounded functions with respect to the posterior distribution of the system parameters computed via the proposed scheme. As a result, we prove, under regularity assumptions, that the approximation errors vanish asymptotically in L p ( p ≥ 1) with convergence rate proportional to 1 √ N + 1 √ M , where N is the number of Monte Carlo samples in the parameter space and N × M is the number of samples in the state space. This result also holds for the approximation of the joint posterior distribution of the parameters and the state variables. We discuss the relationship between the SMC 2 algorithm and the new recursive method and present a simple example in order to illustrate some of the theoretical findings with computer simulations. Keywords: particle filtering, parameter estimation, model inference, state space models, recursive algorithms, Monte Carlo, error bounds.
Issue Date: 1-Nov-2018
Date of Acceptance: 8-May-2017
ISSN: 1350-7265
Publisher: Bernoulli Society for Mathematical Statistics and Probability
Start Page: 3039
End Page: 3086
Journal / Book Title: Bernoulli
Volume: 24
Issue: 4A
Copyright Statement: © 2018 ISI/BS
Sponsor/Funder: Engineering and Physical Sciences Research Council
Funder's Grant Number: EP/N023781/1
Keywords: 0104 Statistics
1403 Econometrics
Statistics & Probability
Publication Status: Published
Online Publication Date: 2018-03-26
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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