Practical filtering with sequential parameter learning

This paper develops a simulation-based approach to sequential parameter learning and filtering in general state-space models. Our approach is based on approximating the target posterior by a mixture of fixedlag smoothing distributions. Parameter inference exploits a sufficient statistic structure and the methodology can be easily implemented by modifying state space smoothing algorithms. We avoid reweighting particles and hence sample degeneracy problems that plague particle filters that use sequential importance sampling. The method is illustrated using two examples: a benchmark autoregressive model with observation error and a high-dimensional dynamic spatio-temporal model. We show that the method provides accurate inference in the presence of outliers, model misspecification and high dimensionality.

[1]  Nicholas G. Polson,et al.  A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling , 1992 .

[2]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[3]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

[4]  S. Frühwirth-Schnatter.  Data Augmentation and Dynamic Linear Models , 1994 .

[5]  N. Shephard,et al.  Stochastic Volatility: Likelihood Inference And Comparison With Arch Models , 1996 .

[6]  G. Kitagawa.  Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models , 1996 .

[7]  Jun S. Liu,et al.  Sequential Monte Carlo methods for dynamic systems , 1997 .

[8]  M. Pitt,et al.  Likelihood analysis of non-Gaussian measurement time series , 1997 .

[9]  N. G. Best,et al.  Dynamic conditional independence models and Markov chain Monte Carlo methods , 1997 .

[10]  S. Chib.  Estimation and comparison of multiple change-point models , 1998 .

[11]  N. Shephard,et al.  Likelihood INference for Discretely Observed Non-linear Diffusions , 2001 .

[12]  P. Bickel,et al.  Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models , 1998 .

[13]  M. Pitt,et al.  Filtering via Simulation: Auxiliary Particle Filters , 1999 .

[14]  Simon J. Godsill,et al.  Fixed-lag smoothing using sequential importance sampling , 1999 .

[15]  Laurent Mevel,et al.  Exponential Forgetting and Geometric Ergodicity in Hidden Markov Models , 2000, Math. Control. Signals Syst..

[16]  Bjørn Eraker.  MCMC Analysis of Diffusion Models With Application to Finance , 2001 .

[17]  Gerhard Tutz,et al.  State Space and Hidden Markov Models , 2001 .

[18]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[19]  Michael K. Pitt,et al.  Auxiliary Variable Based Particle Filters , 2001, Sequential Monte Carlo Methods in Practice.

[20]  Michael A. West,et al.  Combined Parameter and State Estimation in Simulation-Based Filtering , 2001, Sequential Monte Carlo Methods in Practice.

[21]  Genshiro Kitagawa,et al.  Monte Carlo Smoothing and Self-Organising State-Space Model , 2001, Sequential Monte Carlo Methods in Practice.

[22]  S. L. Scott.  Bayesian Methods for Hidden Markov Models , 2002 .

[23]  Geir Storvik,et al.  Particle filters for state-space models with the presence of unknown static parameters , 2002, IEEE Trans. Signal Process..

[24]  M. Pitt.  Smooth Particle Filters for Likelihood Evaluation and Maximisation , 2002 .

[25]  Jonathan R. Stroud,et al.  Sequential Optimal Portfolio Performance: Market and Volatility Timing , 2002 .

[26]  P. Fearnhead.  MCMC, sufficient statistics and particle filters. , 2002 .

[27]  P. Moral,et al.  Sequential Monte Carlo samplers , 2002, cond-mat/0212648.

[28]  Nicholas G. Polson,et al.  Nonlinear State-Space Models With State-Dependent Variances , 2003 .

[29]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[30]  Siem Jan Koopman,et al.  State Space and Unobserved Component Models , 2004 .