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Lookup NU author(s): Takuo Matsubara, Professor Chris Oates
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© 2023 American Statistical Association. Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalization constants requires summation over large or possibly infinite sets, which can be impractical. This article addresses this computational challenge through the development of a novel generalized Bayesian inference procedure suitable for discrete intractable likelihood. Inspired by recent methodological advances for continuous data, the main idea is to update beliefs about model parameters using a discrete Fisher divergence, in lieu of the problematic intractable likelihood. The result is a generalized posterior that can be sampled from using standard computational tools, such as Markov chain Monte Carlo, circumventing the intractable normalizing constant. The statistical properties of the generalized posterior are analyzed, with sufficient conditions for posterior consistency and asymptotic normality established. In addition, a novel and general approach to calibration of generalized posteriors is proposed. Applications are presented on lattice models for discrete spatial data and on multivariate models for count data, where in each case the methodology facilitates generalized Bayesian inference at low computational cost. Supplementary materials for this article are available online.
Author(s): Matsubara T, Knoblauch J, Briol F-X, Oates CJ
Publication type: Article
Publication status: Published
Journal: Journal of the American Statistical Association
Year: 2024
Volume: 119
Issue: 547
Pages: 2345-2355
Online publication date: 12/09/2023
Acceptance date: 30/08/2023
ISSN (print): 0162-1459
ISSN (electronic): 1537-274X
Publisher: Taylor and Francis Ltd
URL: https://doi.org/10.1080/01621459.2023.2257891
DOI: 10.1080/01621459.2023.2257891
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