Department of Statistics, University of Oxford
Week 4: Statistics, Applied Probability & Operational Research Seminars
Date: 3rd November 2011
Venue: Lecture Theatre, Department of Statistics, 1 South Parks Road, Oxford, OX1 3TG
Time: 2:15 p.m.
Tea, coffee and biscuits are served after the seminar in the Statistics Common Room
Speaker: Ajay Jasra<http://2.ic.ac.uk/%7Eaj2/>, Imperial College, London
Title: Sequential Monte Carlo Methods in High Dimensions
Abstract: In the following talk we consider Sequential Monte Carlo (SMC) methods in high dimensions. In particular, the SMC samplers algorithm of Del Moral, Doucet & Jasra (2006) is analyzed in a variety of contexts, as well as SMC methods for the filtering problem, when the dimension d of the target density (or hidden state in filtering) is large. A variety of asymptotic stability properties are established for SMC samplers including: convergence of the expected ESS, the L_p-error of fixed dimensional marginal quantities, propagation of Chaos properties and the behaviour of the relative L_2-error of the estimate of the normalizing constant. These properties are established with a cost of O(Nd^2), N being the number of particles. For the filtering problem, we give an example of an SMC algorithm which stabilizes with a cost of O(n^2 N d^2), n being the time parameter. Unfortunately, this latter algorithm is not useful in online settings. This work constitutes two papers the first with Alex Beskos (UCL) and Dan Crisan (Imperial) and the second with, in addition, to the previous two authors, Nick Whiteley (University of Bristol).
Seminar organiser: Professor Arnaud Doucet <mailto:[log in to unmask]>
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Christine Stone
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Department of Statistics, University of Oxford
1 South Parks Road
Oxford OX1 3TG
Tel: +44 (0)1865 272866/60 Fax: +44 (0)1865 272595
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