SEQUENTIAL MONTE CARLO ALGORITHMS FOR HIGH-DIMENSIONAL FILTERING AND SMOOTHING

Abstract

Hidden Markov models are one of the most successful statistical modelling ideas that provide an extremely flexible framework to handle a variety of complex real-world time series and have countless real applications in bioinformatics, econometrics and finance. However, it is impossible to solve the inference problems of interest for hidden Markov models analytically, except for a small number of simple cases. It is well-known that sequential Monte Carlo methods are a broad and popular class of Monte Carlo algorithms that provide approximate solutions to these intractable inference problems. This thesis aims to make contributions to the developments and applications of sequential Monte Carlo algorithms for the inference problems of hidden Markov models, especially when the dimension of the hidden state space is high. The problems of filtering, smoothing and static parameter estimation are investigated, with the aim to provide efficient and stable sequential Monte Carlo methods for the above-mentioned inference problems.