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Graphical Models, Multivariate Regression and Sparsity, with Applications to Prediction and Macroeconomic Growth Determinant Uncertainty

There has been an explosion in the breadth of information collected in the social sciences, particularly in fields such as economics. In these settings, model uncertainty is a key factor that must be accounted for, and regression variable selection ranks foremost amongst those techniques currently in use. We show that when data exhibit complicated conditional independence relations -- as is frequently the case in the social sciences -- regression variable selection will often perform poorly in comparison to covariance selection techniques based on undirected graphical models. In order to make such comparisons, we build a framework for scoring undirected Gaussian graphical models and show how this can be extended to regression and multivariate regression problems. Through simulation studies, we then show how the use of graphical models and the imposition of sparsity in the conditional independence structure can improve both inference and predictive performance. We conclude with two examples, one multivariate prediction problem as well as an assessment of uncertainty in macroeconomic growth determinants. In each space considered, model search is a major concern and we will also discuss the Mode Oriented Stochastic Search (MOSS) algorithm, which has proven superior to established methods in quickly finding top models.

This is joint work with Theo Eicher and Adrian Dobra.