Seminar | Goulet | Separating epistemic and aleatory uncertainties using conditional BMS
Presenter: James-A Goulet | Professor Polytechnique Montreal
Title: Separating epistemic and aleatory uncertainties using conditional Bayesian model selection
Abstract: The limitations of Bayesian model selection are two-fold: first, the posterior probability mass function (PMF) of models typically wrongfully concentrates the probability mass on a single model, and second this PMF obtained varies greatly across datasets. The hypothesis we will explore in this seminar is that the root cause for these two limitations is the same: the inclusion of the aleatory uncertainties in the likelihood calculations. In practical cases, the variability in the likelihood values induced by the aleatory uncertainties tends to dominate the difference in likelihood between models. As a consequence the likelihood of the aleatory uncertainty wrongfully concentrates the probability content on a single model and induces a large variability across datasets. We will see how the new conditional Bayesian model selection (CBMS) formulation allows separating epistemic and aleatory uncertainty sources so that we represent the posterior PMF of models while excluding aleatory uncertainties from the marginal likelihood calculations. Through the seminar, we will compare the BMS and CBMS methods on case-studies applied on state-space models and Bayesian neural networks.