Models, Idealizations and Objective Chance

Abstract

How does Bayesian inference handle the highly idealized nature of many (statistical) models in science? The standard interpretation of probability as degree of belief in the truth of a model does not seem to apply in such cases since all candidate models are most probably wrong. Similarly, it is not clear how chance-credence coordination works for the probabilities generated by a statistical model. We solve these problems by developing a suppositional account of degree of belief where probabilities in scientific modeling are decoupled from our actual (unconditional) degrees of belief. This explains the normative pull of chance-credence coordination in Bayesian inference, uncovers the essentially counterfactual nature of reasoning with Bayesian models, and squares well with our intuitive judgment that statistical models provide “objective” probabilities.