Philosophy and the practice of Bayesian statistics in the social sciences

Abstract

We view Bayesian data analysis--the iterative process of model building, posterior inference, and model checking--as fitting well within an error-statistics or hypothetico-deductive philosophy of science, with posterior inference playing the role of " normal science, " model checking allowing falsification, and model building providing the potential for progress in normal science (for small changes in a model) or scientific revolutions (for larger re-evaluations). Our practical experience and corresponding philosophy differs in from usual presentations of the philosophy of statistics in two ways. First, we consider posterior probabilities to be a form of scientific measurement rather than as subjective statements of belief. Second, we perform Bayesian model checking by comparing predictions to observed data (in a generalization of classical statistical hypothesis testing), rather than by attempting to compute posterior probabilities of competing models. This chapter presents our own perspective on the philosophy of Bayesian statistics, based on our idiosyncratic readings of the philosophical literature and, more importantly, our experiences doing applied statistics in the social sciences and elsewhere. Think of this as two statistical practitioners' perspective on philosophical and foundational concerns. What we bring to the table are our substantive claims about actual social science research, and we attempt to explain those practices here. We are motivated to write this chapter out of dissatisfaction with what we perceive as the standard view of the philosophical foundations of Bayesian statistics.