Fast, Optimal, and Targeted Predictions Using Parameterized Decision Analysis

Abstract

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. Although classical decision analysis extracts predictions from a Bayesian model, these predictions are often difficult to interpret and slow to compute. Instead, we design a class of parameterized actions for Bayesian decision analysis that produce optimal, scalable, and simple targeted predictions. For a wide variety of action parameterizations and loss functions—including linear actions with sparsity constraints for targeted variable selection—we derive a convenient representation of the optimal targeted prediction 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, or acceptable targeted predictors, which 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 predictions are constructed for physical activity (PA) data from the National Health and Nutrition Examination Survey to better predict and understand the characteristics of intraday PA. Supplementary materials for this article are available online.