Bayesian estimation of linear regression model with unknown prior and noise covariance matrix

0468989 - ÚTIA 2017 IT eng A - Abstrakt
Ulrych, Lukáš - Šmídl, Václav
Bayesian estimation of linear regression model with unknown prior and noise covariance matrix.
ISBA 2016 Book of Abstracts. Cagliari: CUEC, 2016 - (Cabras, S.; Guindani, M.). s. 410-410. ISBN 9-788884-679833.
[ISBA 2016 World meeting. 13.06.2016-17.06.2016, Sardinia]
Grant CEP: GA MŠMT(CZ) 7F14287
Klíčová slova: bayesian statistics * atmospheric transport model * inverse modeling
http://library.utia.cas.cz/separaty/2016/AS/smidl-0468989.pdf

The problem of determination of a source of atmospheric release of pollutant can be formalized as a linear regression problem, y = Mx+e, with two specific features. First, the matrix M is poorly conditioned which require to define prior on the unknown source, x. Second, the covariance matrix of the measurement noise, cov(e) is typically unknown. In this contribution, we study structures of hierarchical priors that could be used to improve estimates of the parameter of interest, x. Inference of all unknowns from the available measurement is not feasible. Therefore, several restrictive parameterizations of the priors are proposed and approximate inference methods are derived for each of them. Specifically, we design models of the measurement covariance matrix with diagonal and block diagonal unknown elements, and with parametric form taking into account possible temporal and spacial correlations. The prior model for x is designed to promote sparse solution, using zero-mean prior with unknown variance. Parameter inference is derived using variational methods and Gibbs sampling. Different variants of the models are them compared using standard model selection techniques on real data from the European tracer experiment.
Trvalý link: http://hdl.handle.net/11104/0269441