Targeted Bayesian Learning

Abstract

TMLE is a loss-based semiparametric estimation method that yields a substitution estimator of a target parameter of the probability distribution of the data that solves the efficient influence curve estimating equation and thereby yields a double robust locally efficient estimator of the parameter of interest under regularity conditions. The Bayesian paradigm is concerned with including the researcher’s prior uncertainty about the probability distribution through a prior distribution on a statistical model for the probability distribution, which combined with the likelihood yields a posterior distribution of the probability distribution that reflects the researcher’s posterior uncertainty. Just like model-based maximum likelihood learning, Bayesian learning is intrinsically nontargeted by working with the prior and posterior distributions of the whole probability distribution of the observed data structure and is thereby very susceptible to bias due to model misspecification or nontargeted model selection.