Discussion: Bayesian Methods: Applied? Yes. Philosophical Defense? In Flux

mistake that the probabilities for any binary trial are 0.5. Would anyone expect that in a random sample of two individuals from California that one would be infected with HIV and the other would not? Or expect that the sun would rise one day and not the next? In addition, uniform priors on the real line, or even normal distributions with mean zero and huge variances, say very silly things, for example, that the parameters are far from zero with high probability. In a logistic regression, such priors induce prior probabilities for events that are concentrated about 50% near zero and about 50% near one (Seaman, Seaman, and Stamey 2012). Pretty stupid. The only advantage to such priors is that they might be easily overwhelmed by data. My advice is to check the implications of one’s prior, uniform or otherwise.