Target-aware Bayesian inference via generalized thermodynamic integration

Fuente: arXiv
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Auteurs principaux: Llorente, F., Martino, L., Delgado, D.
Format: Preprint
Publié: 2025
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author Llorente, F.
Martino, L.
Delgado, D.
author_facet Llorente, F.
Martino, L.
Delgado, D.
contents In Bayesian inference, we are usually interested in the numerical approximation of integrals that are posterior expectations or marginal likelihoods (a.k.a., Bayesian evidence). In this paper, we focus on the computation of the posterior expectation of a function $f(\x)$. We consider a \emph{target-aware} scenario where $f(\x)$ is known in advance and can be exploited in order to improve the estimation of the posterior expectation. In this scenario, this task can be reduced to perform several independent marginal likelihood estimation tasks. The idea of using a path of tempered posterior distributions has been widely applied in the literature for the computation of marginal likelihoods. Thermodynamic integration, path sampling and annealing importance sampling are well-known examples of algorithms belonging to this family of methods. In this work, we introduce a generalized thermodynamic integration (GTI) scheme which is able to perform a target-aware Bayesian inference, i.e., GTI can approximate the posterior expectation of a given function. Several scenarios of application of GTI are discussed and different numerical simulations are provided.
format Preprint
id arxiv_https___arxiv_org_abs_2502_02206
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Target-aware Bayesian inference via generalized thermodynamic integration
Llorente, F.
Martino, L.
Delgado, D.
Computation
Computational Engineering, Finance, and Science
Methodology
In Bayesian inference, we are usually interested in the numerical approximation of integrals that are posterior expectations or marginal likelihoods (a.k.a., Bayesian evidence). In this paper, we focus on the computation of the posterior expectation of a function $f(\x)$. We consider a \emph{target-aware} scenario where $f(\x)$ is known in advance and can be exploited in order to improve the estimation of the posterior expectation. In this scenario, this task can be reduced to perform several independent marginal likelihood estimation tasks. The idea of using a path of tempered posterior distributions has been widely applied in the literature for the computation of marginal likelihoods. Thermodynamic integration, path sampling and annealing importance sampling are well-known examples of algorithms belonging to this family of methods. In this work, we introduce a generalized thermodynamic integration (GTI) scheme which is able to perform a target-aware Bayesian inference, i.e., GTI can approximate the posterior expectation of a given function. Several scenarios of application of GTI are discussed and different numerical simulations are provided.
title Target-aware Bayesian inference via generalized thermodynamic integration
topic Computation
Computational Engineering, Finance, and Science
Methodology
url https://arxiv.org/abs/2502.02206