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2023 Approximate Bayesian Inference Based on Expected Evaluation
Hugo L. Hammer, Michael A. Riegler, Håkon Tjelmeland
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Bayesian Anal. Advance Publication 1-22 (2023). DOI: 10.1214/23-BA1368


Approximate Bayesian computing (ABC) and Bayesian Synthetic likelihood (BSL) are two popular families of methods to evaluate the posterior distribution when the likelihood function is not available or tractable. For existing variants of ABC and BSL, the focus is usually first put on the simulation algorithm, and after that the form of the resulting approximate posterior distribution comes as a consequence of the algorithm. In this paper we turn this around and firstly define a reasonable approximate posterior distribution by studying the distributional properties of the expected discrepancy, or more generally an expected evaluation, with respect to generated samples from the model. The resulting approximate posterior distribution will be on a simple and interpretable form compared to ABC and BSL.

Secondly a Markov chain Monte Carlo (MCMC) algorithm is developed to simulate from the resulting approximate posterior distribution. The algorithm was evaluated on a synthetic data example and on the Stepping Stone population genetics model, demonstrating that the proposed scheme has real world applicability. The algorithm demonstrates competitive results with the BSL and sequential Monte Carlo ABC algorithms, but is outperformed by the ABC MCMC.


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Hugo L. Hammer. Michael A. Riegler. Håkon Tjelmeland. "Approximate Bayesian Inference Based on Expected Evaluation." Bayesian Anal. Advance Publication 1 - 22, 2023.


Published: 2023
First available in Project Euclid: 1 February 2023

Digital Object Identifier: 10.1214/23-BA1368

Keywords: Approximate Bayesian inference , expected evaluation , Markov chain Monte Carlo


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