# Modeling and Simulation Group Meeting Old

#### How can we estimate the slowest dynamics of a Markov process?

**Speaker:**
Robert Webber

**Location:**
TBA

**Date:**
Thursday, April 16, 2020, 1 p.m.

**Synopsis:**

See presentation slides .

When analyzing a Markov process, a frequent goal is identifying the functions of the process that decorrelate most slowly in time. Slowly decorrelating functions are important for dimensionality reduction and prediction, since the values of these functions can be forecast far into the future. Moreover, because of their persistent nature, slowly decorrelating functions often have scientific significance. In biomolecular systems, for example, fluctuations of bond lengths and angles decorrelate quickly, while large-scale rearrangements that determine biological activity generally decorrelate slowly.

Dynamical spectral estimation is a rigorous approach for identifying slowly decorrelating functions. The approach uses sample trajectories to estimate the eigenfunctions of the Markov transition operator. Under appropriate assumptions, a small number of eigenfunctions span all the most slowly decorrelating functions of the process, and the corresponding eigenvalues determine the slowest decorrelation rates.

Despite the prevalence of dynamical spectral estimation in biomolecular simulation studies, estimated eigenfunctions and eigenvalues can have substantial error. The goal of this talk is to identify and bound the major error sources, thereby identifying opportunities where dynamical spectral estimation can produce accurate results.