AMS Weekly Seminar | Benjamin D. Wandelt

Location: Shaffer 3

When: April 23rd at 1:30 p.m.

Title: Cosmology-inspired research themes in statistics and applied math

Abstract: As a way to introduce myself to the department and to start conversations in areas of common research interest, I will present a selection of research vignettes in applied math and statistics that connect to applications in cosmology.

The modeling and analysis of cosmological data pose such problems at considerable scale and structure: Markov Chains on spaces of millions of correlated dimensions; estimating statistics from simulations one cannot afford to run often; performing parameter inference when the likelihood or the prior are intractable but a simulator is available; doing inference of covariance while having a sample of n=1 (one universe!); and working with data on the sphere, the natural domain of whole-sky observations.

I will sketch some threads running through our work on these problems: 1) scalable Bayesian sampling for cosmological fields, from exact Gibbs schemes to posterior sampling of the primordial Universe using Hamiltonian Monte Carlo; 2) numerical harmonic analysis on $S^2$ and $\mathrm{SO}(3)$, including the HEALPix tesselation, exact convolution and sampling theorems; and 3) recasting intractable inference and model comparison tasks as neural optimization problems on graphs and fields. If there is time, I will mention problems involving optimal transport, intrinsic dimensionality estimation, and symbolic regression.

Zoom link: https://wse.zoom.us/j/92366532431