From Robust Tests to Robust Bayes-Like Posterior Distribution

Watch a 31-minute conference talk exploring robust statistical estimation methods for i.i.d. observations within Bayesian statistics, presented at the Centre International de Rencontres Mathématiques in Marseille. Learn about a novel posterior distribution that maintains similarities with classical Bayesian approaches while demonstrating improved stability when dealing with violations in equidistribution assumptions or when data distributions deviate slightly from the model. Discover non-asymptotic results with explicit numerical constants that prove the concentration properties of this new distribution. Recorded during the "Meeting in Mathematical Statistics: New Challenges in High-Dimensional Statistics" conference in December 2024, the presentation includes chapter markers, keywords, abstracts, and bibliographies for enhanced navigation and understanding of the mathematical concepts discussed.