The University of Arizona

What is Bayesian inference, why is it useful in Earth science and why is it challenging to do numerically?

Mathematics Colloquium

What is Bayesian inference, why is it useful in Earth science and why is it challenging to do numerically?
Series: Mathematics Colloquium
Location: MATH 501
Presenter: Matti Morzfeld, University of Arizona

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.

(Refreshments will be served in the Math Commons Room at 3:30 PM)