Gradient angle-based analysis for spatiotemporal point processes

New space/time interaction tests for spatiotemporal point processes

We propose a new test for space-time interaction, using a Mercer kernel-based statistic for measuring the distance between probability distributions. As a concrete example, using a geocoded, time-stamped dataset from Chicago of almost 9 million calls to 911 between 2007 and 2010, we ask whether any of these call types are associated with shootings or homicides nearby in space and time. Standard...

Algorithms for Point Processes Analysis

A time point process can be defined either by the statistical properties of the time intervals between successive points or by those of the number of points in arbitrary time intervals. There are mathematical expressions to link up these two points of view, but they are in many cases too complicated to be used in practice. In this paper we present an algorithmic procedure to obtain the number o...

Residual analysis for spatial point processes

We define residuals for point process models fitted to spatial point pattern data, and propose diagnostic plots based on them. The residuals apply to any point process model that has a conditional intensity; the model may exhibit spatial heterogeneity, interpoint interaction and dependence on spatial covariates. Some existing ad hoc methods for model checking (quadrat counts, scan statistic, ke...

Evaluating spatiotemporal interest point features for depth-based action recognition

Bayesian modeling and analysis for gradients in spatiotemporal processes.

Stochastic process models are widely employed for analyzing spatiotemporal datasets in various scientific disciplines including, but not limited to, environmental monitoring, ecological systems, forestry, hydrology, meteorology, and public health. After inferring on a spatiotemporal process for a given dataset, inferential interest may turn to estimating rates of change, or gradients, over spac...