Adaptive posterior distributions for covariance matrix learning in Bayesian inversion problems for multioutput signals

Ernesto Ángel Curbelo Benítez, Luca Martino, Fernando Llorente Fernández and David Delgado Gómez

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: In this work, we propose an adaptive importance sampling (AIS) scheme for multivariate Bayesian inversion problems, which is based in two main ideas: the inference procedure is divided in two parts and the variables of interest are split in two blocks. We assume that the observations are generated from a complex multivariate non-linear function perturbed by correlated Gaussian noise. We estimate both the unknown parameters of the multivariate non-linear model and the covariance matrix of the noise. In the first part of the proposed inference scheme, a novel AIS technique called adaptive target AIS (ATAIS) is designed, which alternates iteratively between an IS technique over the parameters of the non-linear model and a frequentist approach for the covariance matrix of the noise. In the second part of the proposed inference scheme, a prior density over the covariance matrix is considered and the cloud of samples obtained by ATAIS are recycled and re-weighted for obtaining a complete Bayesian study over the model parameters and covariance matrix. Two numerical examples are presented that show the benefits of the proposed approach.

Keywords: Bayesian; Inversion; Importance; Sampling; Covariance; Matrix; Tempering; Sequence; Of; Posteriors (search for similar items in EconPapers)
Date: 2023-05-30
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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