Elicitation of Uncertainty: Hard and Soft Perspectives - Simon French
Bayesian analysis requires that one addresses many uncertainties, modelling those that can be with subjective probabilities. These probabilities need eliciting either in their entirety or partially via prior distributions which are updated in the light of data during the analysis. Some uncertainties, however, are not easily modelled probabilistically, either because they are deep or because they relate to uncertainties in the modelling process itself. In this paper we discuss the elicitation and communication of all uncertainties to ensure that the users of the analysis are provided with a clear understanding of the residual uncertainties. Moreover, we also consider whose probability should be elicited and addressed by the analysis, arguing that the answer may be different in the varied contexts of Bayesian statistical, risk and decision analyses
A Bayesian MCMC framework for learning and reasoning with staged tree models - Manuele Leonelli
Staged trees are capable of graphically representing a wide array of asymmetric conditional independences between categorical random variables. Both frequentist and Bayesian learning algorithms have been defined which return an optimal staged tree according to a chosen criterion, for instance BIC or MAP. Here we introduce and study the first approximating learning algorithm for staged trees based on a reversible-jump Metropolis-Hastings routine which explores the space of staged tree models. Novel prior distributions over this space are defined and discussed, beyond the standard uniform prior which has been almost exclusively used in MAP estimates. Approximating algorithms return a sample from the posterior distribution of staged tree models. This poses challenges on how to summarize the information of this sample. We adapt methodologies from Bayesian clustering to staged tree models and show how uncertainty statements about asymmetric conditional independences can be constructed. This is joint work with Gherardo Varando.
Continuous time Chain Event Graphs - Jack Carter
I will introduce continuous time processes, the assumptions needed for these to be compactly represented by an event tree and current developments in continuous time chain event graphs.