SCRIPPS INSTITUTION OF OCEANOGRAPHY FACULTY CANDIDATE SEMINAR - Theoretical/Computational Geophysics
DATE: May 21st, Tuesday, 1 p.m.
LOCATION: Eckart 227
SPEAKER: Matthias Morzfeld
University of Arizona
TITLE: What is Bayesian inference, why is it useful in Earth science and why is it challenging to do numerically?
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.