DATE:

Friday, March 6, 2020

TIME:

3:00 PM

LOCATION:

GMCS-314

SPEAKER:

Dr. Henry Scharf, Assistant Professor, Department of Mathematics and Statistics, SDSU

ABSTRACT:

Gaussian processes are a fundamental statistical tool used in a wide range of statistical applications. In the spatio-temporal setting, the covariance of a Gaussian process is typically a function of relative locations in space and time and must satisfy the condition of positive definiteness. Several families of covariance functions exist that attempt to accommodate the wide variety of dependence structures arising in different applications, while ensuring positive definiteness. These parametric families can be restrictive and are insufficient in some situations. In contrast, process convolutions represent a flexible, interpretable approach to defining the covariance of a Gaussian process with modest requirements to ensure validity. We introduce a generalization to the process convolution approach that employs multiple convolutions in sequence to form what we term a “process convolution chain.” In our proposed multi-layered framework, complex dependencies that arise from a combination of different interacting mechanisms are decomposed into a series of interpretable kernel smoothers. We demonstrate an application of process convolution chains to the study of the movement of killer whales, in which the paths taken by multiple individuals are not independent, but reflect dynamic social interactions within the population. We propose a process convolution chain for dependent movement that allows us to make inference about the dynamic social structure in the study population, and to leverage the positive dependence among paths to reduce the uncertainty surrounding the location of an individual during gaps between observations.

HOST:

Jose Castillo

DOWNLOAD: