RT Generic
T1 Adaptive posterior distributions for covariance matrix learning in Bayesian inversion problems for multioutput signals
A1 Curbelo Benitez, Ernesto Angel
A1 Martino, Luca
A1 Llorente Fernandez, Fernando
A1 Delgado Gómez, David
A2 Universidad Carlos III de Madrid. Departamento de Estadística, 
AB 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.
SN 2387-0303
YR 2023
FD 2023-05-30
LK https://hdl.handle.net/10016/37391
UL https://hdl.handle.net/10016/37391
LA eng
DS e-Archivo
RD 17 jun. 2024