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Generalised Bayesian Inference for Discrete Intractable Likelihood

Matsubara, Takuo; Knoblauch, Jeremias; Briol, François-Xavier; Oates, Chris J; (2022) Generalised Bayesian Inference for Discrete Intractable Likelihood. arXiv: Ithaca (NY), USA. Green open access

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Abstract

Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper addresses this computational challenge through the development of a novel generalised 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 generalised posterior that can be sampled using standard computational tools, such as Markov chain Monte Carlo, circumventing the intractable normalising constant. The statistical properties of the generalised posterior are analysed, with sufficient conditions for posterior consistency and asymptotic normality established. In addition, a novel and general approach to calibration of generalised 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 generalised Bayesian inference at low computational cost.

Type: Working / discussion paper
Title: Generalised Bayesian Inference for Discrete Intractable Likelihood
Open access status: An open access version is available from UCL Discovery
Publisher version: https://arxiv.org/abs/2206.08420
Language: English
Additional information: DOI: 10.48550/arXiv.2206.08420. - For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10158243
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