Chair: Tommasi
Giordano, M. Bayesian elliptic inverse problems with Gaussian series priors
Abstract
This work considers the inverse problem of recovering the unknown conductivity function in an elliptic partial differential equation (PDE) from interior measurements of the PDE solution. Nonparametric Bayesian procedures with Gaussian series priors defined on the Dirichlet-Laplacian eigenbasis are devised. Leveraging recent advances from the theory of Bayesian inverse problems, the associated posterior distributions are shown to be asymptotically consistent as the sample size increases, leading to posterior mean estimates with asymptotically vanishing reconstruction errors. An implementation of posterior-based inference is provided via a robust Markov chain Monte Carlo method for functions, and illustrated in a numerical simulation study.
Greca, G. The energy data eco-system
Abstract
Over the last twenty years the energy sector has been characterized by numerous and important changes. The pursuit of new and ambitious energy and environ-mental objectives determines the onset of further changes and the need to have in-formation bases to support the monitoring and development of policies. The cur-rent organization of the statistical offer of the energy sector within SISTAN is based on a division of labor between some highly specialized subjects in the pro-duction and analysis of data within their institutional competence. The exchange and integration of data, as well as the response to requests from international bod-ies (UN, OECD, IEA, Eurostat), are guaranteed by the network of SISTAN sta-tistical offices. However, its further evolution with a view to creating a “data eco-system” will lead several advantages (expansion and differentiation of the output, increase in the coherence, efficiency and timeliness of the data produced, etc.). The energy eco-system data will be instrumental in bridging the information gap relating to the growing demand for statistical information for the achievement of energy and climate objectives and the satisfaction of the information needs of the PNRR, in promptly providing statistical information to policy makers, as well as correctly recording in National accounts support measures in the energy and envi-ronmental fields. This paper proposes the methodological and statistical frame-work for the construction of the energy data eco-system with an output example on energy products.
Pintado, M. F., Iacopini, M., Rossini, L., Shestopaloff, A. Y. Bayesian Markov-Switching Partial Reduced-Rank Regression
Abstract
Reduced-rank (RR) regression is a powerful dimensionality reduction technique, but traditional RR models typically overlook any potential group structure among the responses by assuming a low-rank structure on the coefficient matrix. To address this limitation, a Markov-switching Bayesian Partial RR (MSPRR) regression is proposed. First, the response vector and the coefficient matrix are partitioned into low- and full-rank subgroups. Second, different from traditional approaches assuming known group structure and rank, they are treated as unknown parameters to be estimated. Third, time variation and persistence are accounted for by introducing a Markov-switching process, which examines the changes in the grouping structure and model parameters over time.