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B1725
Title: Using tree-based sampling algorithms in hidden Markov models Authors:  Dong Ding - Imperial College London (United Kingdom) [presenting]
Axel Gandy - Imperial College London (United Kingdom)
Abstract: A recently proposed algorithm called divide-and-conquer sequential Monte Carlo splits a probabilistic model into small parts, samples the particles independently in these parts and subsequently merges the particles in a tree structure. A hidden Markov model is a stochastic process where the hidden process is a Markov process and the observations are independent given the hidden states. We investigate using the divide-and-conquer sequential Monte Carlo algorithm in such models. We investigate how it can be used for standard particle filtering, particle smoothing and sampling from the joint distribution of the hidden states given all the observations. We use two algorithms to generate and merge the samples. In both algorithms, we first run a standard bootstrap particle filter. The first approach uses the samples from the particle filter directly and the second approach constructs a parametric approximation. We study adaptive methods for improving the initial and the intermediate target distributions in the tree. We illustrate the performance in a simulation study.