Abstract and Keywords
This article discusses the Bayesian approach to decision theory. It focuses on the case of an individual deciding between treatments. It deals with the role of information that is available about other individuals through a propensity score. It also shows the reason for absence of propensity score in the likelihood function but its appearance in the prior. A prior distribution leads to a closed-form expression for the decision rule. The parametric model plays the role of a prior distribution that can be dominated by the data. The next section examines the role of the propensity score in a random effects model with normal distributions for the outcomes and the random effects. It takes up the extension to the case of treatment selection based on unobservables. The main aim of this article is to estimate an average treatment effect for a particular covariate cell.
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