Sequential Monte Carlo smoothing for general state space hidden Markov models

Abstract

Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a foundation of particle-based approximation of such distributions and to analyze, in a common unifying framework, different schemes producing such approximations. In this setting, general convergence results, including exponential deviation inequalities and central limit theorems, are established. In particular, time uniform bounds on the marginal smoothing error are obtained under appropriate mixing conditions on the transition kernel of the latent chain. In addition, we propose an algorithm approximating the joint smoothing distribution at a cost that grows only linearly with the number of particles.

Published in at http://dx.doi.org/10.1214/10-AAP735 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1012.4183 by other authors

References in corpus (6)

• Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference
• Recursive Monte Carlo filters: Algorithms and theoretical analysis
• Uniform observability of hidden Markov models and filter stability for unstable signals
• Uniform Time Average Consistency of Monte Carlo Particle Filters
• The stability of conditional Markov processes and Markov chains in random environments
• Stability of nonlinear filters in nonmixing case

Cited by in corpus (38)

• On Particle Methods for Parameter Estimation in State-Space Models
• Three discussions of the paper "sequential quasi-Monte Carlo sampling", by M. Gerber and N. Chopin
• Particle Filters and Data Assimilation
• Stability properties of some particle filters
• Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods
• Rao-Blackwellized particle smoothers for conditionally linear Gaussian models
• Sequential Monte Carlo Methods for System Identification
• Long-term stability of sequential Monte Carlo methods under verifiable conditions
• Particle Smoothing for Hidden Diffusion Processes: Adaptive Path Integral Smoother
• Modelling multi-scale state-switching functional data with hidden Markov models
• Approximate Smoothing and Parameter Estimation in High-Dimensional State-Space Models
• On the use of backward simulation in particle Markov chain Monte Carlo methods
• Particle approximation improvement of the joint smoothing distribution with on-the-fly variance estimation
• Smoothing distributions for conditional Fleming-Viot and Dawson-Watanabe diffusions
• Nonlinear state space smoothing using the conditional particle filter
• Fast and numerically stable particle-based online additive smoothing: the AdaSmooth algorithm
• Online Particle Smoothing with Application to Map-matching
• Online Smoothing for Diffusion Processes Observed with Noise
• Online Sequential Monte Carlo smoother for partially observed stochastic differential equations
• Efficient particle-based online smoothing in general hidden Markov models: the PaRIS algorithm
• Particle-based adaptive-lag online marginal smoothing in general state-space models
• Resampling Algorithms for High Energy Physics Simulations
• A Bayesian nonparametric approach for generalized Bradley-Terry models in random environment
• Double Bayesian Smoothing as Message Passing
• A Sharp First Order Analysis of Feynman-Kac Particle Models
• A State-Space Perspective on Modelling and Inference for Online Skill Rating
• Approximate Bayesian Computation for Smoothing
• On Unbiased Score Estimation for Partially Observed Diffusions
• Metropolising forward particle filtering backward sampling and Rao-Blackwellisation of Metropolised particle smoothers
• NEO: Non Equilibrium Sampling on the Orbit of a Deterministic Transform
• On-line Bayesian parameter estimation in general non-linear state-space models: A tutorial and new results
• Amortized backward variational inference in nonlinear state-space models
• Convergence of Sequential Quasi-Monte Carlo Smoothing Algorithms
• An efficient particle-based online EM algorithm for general state-space models
• Particle-based likelihood inference in partially observed diffusion processes using generalised Poisson estimators
• Efficient parameter inference in general hidden Markov models using the filter derivatives
• Rao-Blackwellized Particle Smoothing as Message Passing
• Calculating principal eigen-functions of non-negative integral kernels: particle approximations and applications