### Mathematics Colloquium

** 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?

**Date:** Friday, September 6, 2019

**Place and Time:** Room 101, Love Building, 3:35-4:25 pm

**Refreshments:** Room 204, Love Building, 3:00 pm

**Abstract.**
I will first review Bayesian inference, which means to incorporate information from observations (data) into a numerical model, and will give some examples of applications in Earth science. The numerical solution of Bayesian inference problems 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.