Multivariate Bayesian dynamic modeling for causal prediction

Abstract: Bayesian forecasting is developed in multivariate time series analysis for causal inference. Causal evaluation of sequentially observed time series data from control and treated units focuses on the impacts of interventions using contemporaneous outcomes in control units. Methodological developments here concern multivariate dynamic models for time-varying effects across multiple treated units with explicit foci on sequential learning and aggregation of intervention effects. Analysis explores dimension reduction across multiple synthetic counterfactual predictors. Computational advances leverage fully conjugate models for efficient sequential learning and inference, including cross-unit correlations and their time variation. This allows full uncertainty quantification on model hyper-parameters via Bayesian model averaging. A detailed case study evaluates interventions in a supermarket promotions experiment, with coupled predictive analyses in selected regions of a large-scale commercial system. Comparisons with existing methods highlight the issues of appropriate uncertainty quantification in casual inference in aggregation across treated units, among other practical concerns.