Title: General Bayesian inference
Authors: Pier Giovanni Bissiri - - (Italy) [presenting]
Chris Holmes - University of Oxford (United Kingdom)
Stephen Walker - University of Texas at Austin (United States)
Abstract: A coherent procedure is considered for general Bayesian inference based on updating a prior belief distribution to a posterior when the parameter of interest is connected to observations via a loss function. If such loss is the negative log-likelihood, then the Bayesian approach is recovered as a natural special case. This general updating process follows from a decision-theoretic approach involving cumulative loss functions where the Kullback-Leibler divergence plays a central role. Moreover, it is the only updating mechanism satisfying a coherence property together with some other natural assumptions.