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Seminar

Flow Transport SMC Samplers

Thursday, June 14, 2018 5:15 PM;

JGU Mainz, Mathematics, Hilbert-Raum

Speaker: Yvo Pokern; University College London, UK

After introducing the problem of sampling from complex posterior distributions for a statistical parameter of interest given observed data arising in Bayesian computational statistics, I will present an overview of sequential Monte Carlo methods, also known as particle filters. One of the main challenges of this class of methods is the design of proposals, i.e. of a stochastic process that strikes a balance between traversing the relevant regions of parameter space but sticking to proposed parameter values that fit the data acceptably well. A novel proposal based on approximate mass transport considerations is then described: gradually introducing the likelihood to move from the prior to the posterior distribution via a simulated annealing temperature schedule gives rise to a curve of target measures. The evolution of these measures is captured in a Liouville equation. An approximate solution to this Liouville equation is proposed that requires only the evaluation of one-dimensional integrals via particle approximations. The vector field thus obtained yields ordinary differential equation proposal dynamics that target posterior modes well in applied examples. Partial results on approximation error bounds are presented along with applications to mixture modeling and truncated Gaussians.

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