University of Washington - Department of Statistics
We develop a framework for the modeling of high-dimensional data that is robust to a variety of data types and modeling paradigms. In particular, we focus on several classes of models that each employ conditional independence assumptions to derive estimators. In this presentation we pay particular attention to the problem of model averaging in instrumental variable models, which rely on conditional independence assumptions between subsets of variables to form estimators possessing desirable properties for causal inference. We extend the Bayesian Model Averaging (BMA) approach for regression variable selection and develop an Instrumental Variable BMA (IVBMA) approach that incorporates both instrument and variable uncertainty into the IV framework. We show that IVBMA estimators possess a number of desirable features over standard IV estimators. Furthermore, we propose a class of tests of model assumptions based on the model averaging of predictive p-values which have dramatically improved power over classical tests of IV assumptions proposed in the econometrics literature. We conclude with a discussion of ongoing and future research topics, including embedding Gaussian Graphical Models in Dirichlet Mixture Processes and the modeling of changing interaction regimes in foreign exchange markets through the infinite-dimensional Hidden Markov Model (iHMM).