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Seminar 23 October 2020 @2pm

Dynamic fibre samplers for linear inverse problems

Date: 23 October 2020, Friday

Time: 2pm

Speaker: Prof. Martin Hazelton (University of Otago, New Zealand)

Abstract:

Statistical inverse problems occur when we wish to learn about some random process that is observed only
indirectly. Inference in such situations typically involves sampling possible values for the latent variables
of interest conditional on the indirect observations. This talk is concerned with linear inverse problems for
count data, for which the latent variables are constrained to lie on a fibre (solution set for the linear system) comprising the integer lattice within a convex polytope (a bounded multidimensional polyhedron). An illustrative example arises in transport engineering where we observe vehicle counts entering or leaving each zone of the network, then want to sample possible interzonal patterns of traffic flow consistent with those entry/exit counts. Other areas of application include estimation of non-compliance rates in biosecurity surveillance, and capture-recapture modelling in ecology.

Such sampling can be conducted using Markov chain Monte Carlo methods, through a random walk on the fibre. A major challenge is finding a set of basic moves (sampling directions) so as to ensure that
the walk can connect any two feasible points without leaving the fibre. In principle this can be done by
computing a Markov basis of potential moves, but in practice the resulting sampler can be hugely inefficient even when such a basis is computable. In this talk I will describe some current work on developing a dynamic Markov basis that generates moves on the fly. This approach can guarantee irreducibility of the sampler while gaining efficiency by increasing the probability of selecting serviceable sampling directions.

Link: https://au.bbcollab.com/guest/fcf219c74ac743e89565a9e6e8d349a9

Video: