Adaptive quadrature schemes for Bayesian inference via active learning

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Show simple item record Llorente Fernandez, Fernando Martino, Luca Elvira Arregui, Víctor Delgado Gómez, David López Santiago, Javier
dc.contributor.editor Universidad Carlos III de Madrid. Departamento de Estadística 2020-06-08T11:05:08Z 2020-06-08T11:05:08Z 2020-05-29
dc.identifier.issn 2387-0303
dc.description.abstract Numerical integration and emulation are fundamental topics across scientific fields. We propose novel adaptive quadrature schemes based on an active learning procedure. We consider an interpolative approach for building a surrogate posterior density, combining it with Monte Carlo sampling methods and other quadrature rules. The nodes of the quadrature are sequentially chosen by maximizing a suitable acquisition function, which takes into account the current approximation of the posterior and the positions of the nodes. This maximization does not require additional evaluations of the true posterior. We introduce two specific schemes based on Gaussian and Nearest Neighbors (NN) bases. For the Gaussian case, we also provide a novel procedure for fitting the band width parameter, in order to build a suitable emulator of a density function. With both techniques, we always obtain a positive estimation of the marginal likelihood (a.k.a., Bayesian evidence). An equivalent importance sampling interpretation is also described, which allows the design of extended schemes. Several theoretical results are provided and discussed. Numerical results show the advantage of the proposed approach, including a challenging inference problem in an astronomic dynamical model, with the goal of revealing the number of planets orbiting a star.
dc.language.iso eng
dc.relation.ispartofseries Working paper. Statistics and Econometrics
dc.relation.ispartofseries 20-03
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.subject.other Numerical Integration
dc.subject.other Emulation
dc.subject.other Monte Carlo Methods
dc.subject.other Bayesian Quadrature
dc.subject.other Experimental Design
dc.subject.other Active Learning
dc.title Adaptive quadrature schemes for Bayesian inference via active learning
dc.type workingPaper
dc.identifier.uxxi DT/0000001758
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