Weakly Informative Priors
Weakly Informative Priors
by Andrew Gelman
This project proposes the development of practical tools for routine data analysis using Bayesian inference with weakly informative priors, which represent a way to add a small amount of information to stabilize a statistical analysis without overwhelming the information in the data. This is a key theme in signal processing. At the theoretical level, it will unify the choice of prior distribution by placing noninformative and weakly informative priors into a common framework of hierarchical modeling. Methodologically speaking, the models will be programmed using the EM algorithm, the Gibbs sampler, and the metropolis algorithm. Because of the additional information in these models, consumption should ultimately be more stable than with classical methods based on least squares, maximum likelihood, and noninformative priors. As an innovation in statistical computing, we propose to include automatic unit testing and cross validation in our implementations. We also propose to use the cross-validation to evaluate the performance of our methods on corpuses of datasets. For applications, we propose to fit our models in ongoing research efforts in public opinion, social networks, and public health, among others. In addition to their inherent interest, these applications will allow us to understand the practical gains arising from our methods and will motivate others to develop further work in this area.
