Replica Exchange Particle-Gibbs Method with Ancestor Sampling

Koji Hukushima,Toshiaki Omori,Hiroaki Inoue

doi:10.7566/jpsj.89.104801

Abstract

Particle-Gibbs (PG) method is a Markov chain Monte Carlo (MCMC) method for sampling from the joint posterior distribution of latent variables and parameters in a nonlinear state space model, which ...

Highlights

In recent years, time-series data have been investigated extensively by using state space models.1–18) State space models are probabilistic models that assume the existence of latent variables
It becomes possible to prevent increasing the calculation time because each particle-Gibbs with ancestor sampling (PGAS) is able to be run in parallel. It is shown by employing our replica exchange particle-Gibbs with ancestor sampling (REPGAS) for the benchmark nonlinear state space model, that the joint posterior distribution of latent variables and parameters can be estimated from observations, that sampling efficiency is improved compared to PGAS, and that it is possible to overcome the problem of initial value dependence in PGAS
We have proposed REPGAS, a method for estimating the joint posterior distribution of latent variables and parameters in a state space model

Summary

Introduction

Time-series data have been investigated extensively by using state space models.1–18) State space models are probabilistic models that assume the existence of latent variables. In the state space models, we assume a system model describing dynamical behavior of latent variables and an observation model describing a process that relates latent variables to observation values. If the values of the model parameters are unknown, it is necessary to estimate the parameters and latent variables in the state space model simultaneously. A method combining a sequential Bayesian filter and expectation–maximization (EM) algorithm has been employed to estimate latent variables and parameters of state space models.2,7,9,15,20,21) the method is an iterative method for point estimation of parameters and its convergence to a local optimum is guaranteed, its dependence on the initial value makes it hard for it to estimate a global optimum in a complex state space model

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