Curbelo Benitez, Ernesto AngelMartino, LucaLlorente Fernandez, FernandoDelgado Gómez, DavidUniversidad Carlos III de Madrid. Departamento de Estadística2023-05-302023-05-302023-05-302387-0303https://hdl.handle.net/10016/37391In 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.engAtribución-NoComercial-SinDerivadas 3.0 EspañaBayesian InversionImportance SamplingCovariance MatrixTemperingSequence Of Posteriorsworking paperEstadísticaDT/0000002075