Statistical inference with external information: high-dimensional data integration

D. Rossell, P. Rognon, P. Zwiernick

Statistical inference when there are many parameters has fundamental limits in what types of signals one may learn from data, e.g. minimal sample sizes, signal strength or sparsity conditions. There are many applied problems however where, besides the data directly being analyzed, one has access to external data that may help improve inference. Examples include data integration and high-dimensional causal inference, where formally incorporating external information has shown significant practical benefits. We discuss some of these situations, use graphical models for COVID19 evolution and causal inference for gender salary gaps, and provide a theoretical analysis in a simplified Gaussian sequence model. The latter shows that, by integrating external information, one may push the theoretical limits of what's possible to learn from data, providing a theoretical justification for this popular applied practice.

Keywords: Bayesian inference, data integration, asymptotics, graphical models, regression

GT11.BAYES1 Variable Selection
November 7, 2023  4:50 PM
CC1: Audience

V. Peña

G. Garcia-Donato, M. E. Castellanos Nueda

S. Cabras, M. E. Castellanos Nueda, A. Forte Deltell, G. Garcia-Donato, A. Quirós Carretero