Seminar on Probability and Statistics

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Organizer(s) Nakahiro Yoshida, Hiroki Masuda, Teppei Ogihara, Yuta Koike

2022/01/19

14:30-16:00   Room # (Graduate School of Math. Sci. Bldg.)
Martin Hazelton (Otago University)
Dynamic fibre samplers for linear inverse problems
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)
https://sites.google.com/view/apsps/home

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. For count data, the latent variables are constrained to lie on a fibre (solution set for the linear system) comprising the integer lattice within a convex polytope.

Sampling the latent counts can be conducted using MCMC methods,through a random walk on this fibre. A major challenge is finding a set of basic moves that ensures connectedness of the walk over the fibre. In principle this can be done by computing a Markov basis of potential moves, but 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.
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLSeoXt5v8xdQNFAKTDLoD0lttaHjV17_r7864x11mtxU1EQlhQ/viewform