Statistical Methods and Extreme Events in Climate

Prediction of extreme weather/climate events from historical observations is a critical challenge, both because those events have tremendous societal impact, and because they are rare, or even absent, from training data. In principle, physical models can be used to generate rare or previously unobserved events. However, accurate physical models are too costly to run for the long time scales required to generate very rare events. Recently, AI prediction models have generated significant interest. One of their primary advantages relative to physical models is their greatly reduced cost to generate a forecast, raising the possibility that these models can be used to interrogate far into the tails of weather and climate distributions. After formaly introducing the rare event prediction problem, we will cover a mix of empirical and mathematical results that bring the boundaries of AI extreme event prediction into sharper focus. We will address two key questions: Can AI methods predict events not seen in their training distributions? and Which AI methods make efficient use of the data we have for rare event prediction and which do not?