The 2015 Q4 issue of SIAM Review will carry an article by Houman Owhadi, Clint Scovel, and myself on the brittle dependency of Bayesian posteriors as a function of the prior. This is an abbreviated presentation of results given in full earlier this year in Elec. J. Stat. The PDF is available for free under the terms of the Creative Commons 4.0 licence.
H. Owhadi, C. Scovel & T. J. Sullivan. “On the Brittleness of Bayesian Inference” SIAM Review 57(4):566–582, 2015. doi:10.1137/130938633
The 2013 Q2 issue of SIAM Review will carry an article by Houman Owhadi, Clint Scovel, Mike McKerns, Michael Ortiz and myself on the optimization approaches to uncertainty quantification in the presence of infinite-dimensional epistemic uncertainties about the probability measures and response functions of interest.
We present both a mathematical framework for the reduction of such infinite-dimensional problems to finite-dimensional effective feasible sets, and apply the methods to practical examples arising in hypervelocity impact and seismic safety certification.
H. Owhadi, C. Scovel, T. J. Sullivan, M. McKerns & M. Ortiz. “Optimal Uncertainty Quantification.” SIAM Review 55(2):271–345, 2013. doi:10.1137/10080782X