Title: Bayesian uncertainty
Authors: Stephen Walker - University of Texas at Austin (United States) [presenting]
Chris Holmes - University of Oxford (United Kingdom)
Edwin Fong - University of Oxford (United Kingdom)
Abstract: It is argued that quantifying Bayesian uncertainty is concerned with placing a distribution on the missing data, which, if known, the parameter of interest would be fully known. Hence, the missing data arise from the usual observations being a finite sample. Under certain assumptions on the distribution for the missing data, it is possible to recover the usual posterior distribution. With alternative assumptions, e.g. replacing exchangeability for conditionally identically distributed, we derive ``posterior'' distributions obtained as limits of martingale sequences. Illustrations will be presented.