W 911 Nf - 15 - 1 - 0154 66552 - Ma - Ii . 4 312 - 413 - 2156

Number of Papers published in peer-reviewed journals: Number of Papers published in non peer-reviewed journals: Final Report: Variations on Bayesian Prediction and Inference Report Title A Bayesian approach, based on updating prior information in light of new observations, via Bayes's formula, has both nice intuition and strong theoretical support. However, in some applications, there are some roadblocks to carrying out the Bayesian analysis as usual. This ARO-sponsored project considered two general types of these settings. First, for the problem of predicting a future observation, a flexible Bayesian model is available but is too computationally expensive to implement when data are streaming and fast prediction is required. Second, for the problem of inference about an unknown parameter, the Bayesian approach requires a full probability model/likelihood which can be an obstacle; indeed, there are applications where no likelihood function is available or, even in cases where a likelihood is or could be made available, it may be preferable not to use it because it depends on nuisance parameters, etc. Work done in this project addresses both the prediction and inference problems, expanding the range of applications of the Bayesian approach to help meet the Army's needs. (a) Papers published in peer-reviewed journals (N/A for none) Enter List of papers submitted or published that acknowledge ARO support from the start of the project to the date of this printing. List the papers, including journal references, in the following categories: (b) Papers published in non-peer-reviewed journals (N/A for none) My student, Nick Syring, has presented his work done in the paper "Scaling the Gibbs posterior credible regions" in our department's Statistics Seminar. He will also be presenting his work in the paper "Image boundary detection via a Gibbs posterior" at the end of May 2016 at the Spring Research Conference being held at Illinois Institute of Technology. My collaborator (Stephen Walker) has presented, on several occasions, our work in the paper "On recursive Bayesian predictive distributions". (c) Presentations Received Paper