Date of Award

Spring 2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

Norou Diawara

Committee Member

N. Rao Chaganty

Committee Member

Kayoung Park

Committee Member

Bryan Porter

Abstract

Moran's index is a statistic that measures spatial dependence, quantifying the degree of dispersion or clustering of point processes and events in some location/area. Recognizing that a single Moran's index may not give a sufficient summary of the spatial autocorrelation measure, a local indicator of spatial association (LISA) has gained popularity. Accordingly, we propose extending LISAs to time after partitioning the area and computing a Moran-type statistic for each subarea. Patterns between the local neighbors are unveiled that would not otherwise be apparent. We consider the measures of Moran statistics while incorporating a time factor under simulated multilevel Palm distribution, a generalized Poisson phenomenon where the clusters and dependence among the subareas are captured by the rate of increase of the process over time. Event propagation is built under spatial nested sequences over time. The Palm parameters, Moran statistics and convergence criteria are calculated from an explicit algorithm in a Markov chain Monte Carlo simulation setting and further analyzed in two real datasets.

DOI

10.25777/3mps-rk62

ISBN

9781392268087

ORCID

0000-0002-4668-9048

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