Discussion Papers 2021

CIRJE-F-1175	"Particle Rolling MCMC with Double-Block Sampling "
Author Name	Awaya, Naoki and Yasuhiro Omori
Date	September 2021
Full Paper	PDF file
Remarks	Revised Version of CIRJE-F-1066(2017), CIRJE-F-1080(2018), CIRJE-F-1110(2019) and CIRJE-F-1126(2019); Published in Japanese Journal of Statistics and Data Science, 6, 305-335. DOI: 10.1007/s42081-022-00170-2

Abstract
An efficient particle Markov chain Monte Carlo methodology is proposed for the rollingwindow estimation of state space models. The particles are updated to approximate the long sequence of posterior distributions as we move the estimation window. To overcome the wellknown weight degeneracy problem that causes the poor approximation, we introduce a practical double-block sampler with the conditional sequential Monte Carlo update where we choose one lineage from multiple candidates for the set of current state variables. Our proposed sampler is justified in the augmented space through theoretical discussions. In the illustrative examples, it is shown to be successful to accurately estimate the posterior distributions of the model parameters.
Keywords: Double-block sampler; Forward and backward sampling; Importance sampling; Particle Gibbs; Particle Markov chain Monte Carlo; Particle simulation smoother; Rolling-window estimation; Sequential Monte Carlo; State space model; Structural change

Abstract

An efficient particle Markov chain Monte Carlo methodology is proposed for the rollingwindow estimation of state space models. The particles are updated to approximate the long sequence of posterior distributions as we move the estimation window. To overcome the wellknown weight degeneracy problem that causes the poor approximation, we introduce a practical double-block sampler with the conditional sequential Monte Carlo update where we choose one lineage from multiple candidates for the set of current state variables. Our proposed sampler is justified in the augmented space through theoretical discussions. In the illustrative examples, it is shown to be successful to accurately estimate the posterior distributions of the model parameters.

Keywords: Double-block sampler; Forward and backward sampling; Importance sampling; Particle Gibbs; Particle Markov chain Monte Carlo; Particle simulation smoother; Rolling-window estimation; Sequential Monte Carlo; State space model; Structural change