Hazelton, Martin

Approximate samplers for linear inverse problem

Martin Hazelton, Mike McVeagh, and Bruce van Brunt

Institute of Fundamental Sciences, Massey University, Palmerston North

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 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 inference for contingency tables, and capture-recapture modelling in ecology.

In principle such sampling can be conducted using Markov chain Monte Carlo methods, through a random walk on the lattice polytope. However, it is challenging to design algorithms for exact sampling that are both scalable and have guaranteed theoretical properties. In this talk I will describe some current work on developing approximate samplers that are nonetheless guaranteed to connect all lattice points carrying appreciable posterior probability.