From Monte Carlo to Climate: A Journey through Probabilistic Inference

Abstract:
Bayesian inference offers a principled framework for learning and prediction under uncertainty, but putting it into practice raises fundamental modelling and computational challenges. We begin with Monte Carlo and importance sampling, where the challenge is to approximate otherwise intractable inference, and move to state-space models, where the quantities of interest are hidden and evolve over time. From there, we consider what happens when the events we want to predict are so rare that standard simulation may never see them, when the model itself is uncertain, and when algorithms must adapt their computational effort. These methodological questions are relevant in climate science, where forecasting tipping points, such as abrupt changes in the North Atlantic Ocean, brings many of these challenges together: limited observations, uncertain and computationally expensive models, multiple spatial and temporal scales, and rare transitions with large consequences.