We are pleased to announce an upcoming talk by Dr. Marcelo Hartmann from the University of Helsinki, who will be presenting on May 15, 2025, at 16:15.
The Bayesian paradigm for statistical inference has been widely used across many areas of scientific research. However, the increasing complexity of models used in practice makes the Bayes formula hard to compute. As a result, any quantity of interest that depends on the posterior measure becomes difficult to infer.
In this talk, we present inference methods that leverage concepts from differential geometry to enhance classical tools for posterior analysis. The central idea is to select an appropriate geometry for the parameter space, encoded through a metric tensor (a (0,2)-tensor). By choosing the metric tensor induced by the embedding of the log-posterior graph, we can obtain computational benefits, though at the cost of a slightly less accurate representation of the underlying geometry and thus slight less accurate with respect to the exact posterior inference. We illustrate this trade-off in the context of Riemann-Laplace approximation, comparing the classical Fisher information metric with the embedding metric, which we call Monge metric. Finally, we outline future directions, particularly using of more general geometric frameworks through the more general inference theory of Godambe’s theory of estimating functions.
