On-line inference for hidden Markov models via particle filters


  • Paul Fearnhead,

  • Peter Clifford

Paul Fearnhead, Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster, LA1 4YF, UK.
E-mail: p.fearnhead@lancaster.ac.uk


Summary.  We consider the on-line Bayesian analysis of data by using a hidden Markov model, where inference is tractable conditional on the history of the state of the hidden component. A new particle filter algorithm is introduced and shown to produce promising results when analysing data of this type. The algorithm is similar to the mixture Kalman filter but uses a different resampling algorithm. We prove that this resampling algorithm is computationally efficient and optimal, among unbiased resampling algorithms, in terms of minimizing a squared error loss function. In a practical example, that of estimating break points from well-log data, our new particle filter outperforms two other particle filters, one of which is the mixture Kalman filter, by between one and two orders of magnitude.