Fast and Optimal Bayesian Approximations for Targeted Prediction

Prediction is critical for decision-making under uncertainty and lends validity to statistical inference. With targeted prediction, the goal is to optimize predictions for specific decision tasks of interest, which we represent via functionals. Using tools for predictive decision analysis, we design a framework for constructing optimal, scalable, and simple approximations for targeted prediction under a Bayesian model. For a wide variety of approximations and (penalized) loss functions, we derive a convenient representation of the optimal targeted approximation that yields efficient and interpretable solutions. Customized out-of-sample predictive metrics are developed to evaluate and compare among targeted predictors. Through careful use of the posterior predictive distribution, we introduce a procedure that identifies a set of near-optimal predictors. These acceptable models can include different model forms or subsets of covariates and provide unique insights into the features and level of complexity needed for accurate targeted prediction. Simulations demonstrate excellent prediction, estimation, and variable selection capabilities. Targeted approximations are constructed for physical activity data from the National Health and Nutrition Examination Survey (NHANES) to better predict and understand the characteristics of intraday physical activity.