Weakly Informative Priors: When a little information can do a lot of regularizing

A challenge in statistics is to construct models that are structured enough to be able to learn from data but not be so strong as to overwhelm the data. We introduce the concept of "weakly informative priors" which contain important information but less than may be available for the given problem at hand. We discuss weakly informative priors for logistic regression coefficients, hierarchical variance parameters, covariance matrices, and other models, in various applications in social science and public health. I think this is an extremely important idea that should change how we think about Bayesian models.