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|Title:||SEQUENTIAL MONTE CARLO FOR BAYESIAN INFERENCE AND DATA ASSIMILATION||Authors:||DEBORSHEE SEN||Keywords:||Particle filter, MCMC, option pricing, optimal transport, parallelisation, alpha-SMC||Issue Date:||21-Aug-2017||Citation:||DEBORSHEE SEN (2017-08-21). SEQUENTIAL MONTE CARLO FOR BAYESIAN INFERENCE AND DATA ASSIMILATION. ScholarBank@NUS Repository.||Abstract:||This thesis consists of three main parts. The first is an application of sequential Monte Carlo (SMC) methods, also known as particle filters, to option pricing. In particular, a sequence of weighting functions is constructed in order to approximate the optimal importance sampling distribution. The second part is mainly methodological in which a framework for coupling particle filters is developed. Ideas from optimal transport literature are utilised to build an efficient coupled-resampling step. Computationally tractable approximations to optimal transport couplings are introduced to speed things up. The third part is mainly theoretical and concerns parallelising particle filters. A recent algorithm known as alpha-SMC is considered and its time-uniform stability is related to the spectral gap of its underlying communication structure. An asymptotic analysis is also provided and it is proved that the alpha-SMC algorithm can be asymptotically equivalent to an algorithm with a complete graph, even for extremely sparse graphs.||URI:||http://scholarbank.nus.edu.sg/handle/10635/138982|
|Appears in Collections:||Ph.D Theses (Open)|
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