Faculty Candidate Seminar - Matthias Morzfeld

Bayesian inference is used to update the predictions of computational models based on observations. I will first give three examples of Bayesian inference in Earth science: (i) predicting reversals of Earth’s magnetic axial dipole; (ii) intra-hour forecasting of global horizontal irradiance for use in solar power forecasts; and (iii) connecting a “phenomenological” predator-prey model for stratocumulus cloud desks to large eddy simulations.

 

The second part of the talk describes the numerical solution of Bayesian inference problems, which is often based on sampling a posterior probability distribution. Sampling posterior distributions is difficult because these are usually high-dimensional (many parameters or states to estimate) and non-standard (e.g., not Gaussian). In particular a high-dimension causes numerical difficulties and slow convergence in many sampling algorithms. I will explain how ideas from numerical weather prediction can be leveraged to design Markov chain Monte Carlo (MCMC) samplers whose convergence rates are independent of the problem dimension for a well-defined class of problems. This will lead to a “map” of characteristics that make Bayesian inference problems numerically feasible to solve.