Activity Number:

80
 Advancement in Spatial and Spatiotemporal Point Process

Type:

Contributed

Date/Time:

Sunday, July 29, 2018 : 4:00 PM to 5:50 PM

Sponsor:

Section on Statistics and the Environment

Abstract #330193

Presentation

Title:

Velocities for Point Patterns

Author(s):

Erin Schliep* and Alan E Gelfand

Companies:

University of Missouri and Duke University

Keywords:

directional derivatives;
logGaussian Cox process;
spatiotemporal

Abstract:

The aim of a spatiotemporal point pattern analysis is to develop an understanding of the interaction of events across a landscape over time. We propose a novel inferential metric of spatiotemporal point patterns using spatial and temporal gradients. These gradients describe the instantaneous change in the probability of an event in a specified direction (space) and time. The ratio of the temporal gradient to the spatial gradient is then the change in probability of an event per unit time over the change in probability of an event per unit distance. This becomes the relative change in risk in units of distance per time, or, a velocity for the point pattern. We illustrate our approach using a spatiotemporal point pattern of crime data from an urban city to obtain estimates of the velocity of crime. The approach has wide application in estimating the velocity of a disease epidemic or a species distribution across a region as a response to a changing environment.
