Spatio-Temporal Cluster Detection and Local Moran Statistics of Point Processes

<p>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.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics & Statistics

Year dc:date.available

2019

Author dc:creator

• Matthews, Jennifer L.

Contributors dc:contributor

• Norou Diawara
• N. Rao Chaganty
• Kayoung Park
• Bryan Porter

• Moran's index
• Point processes
• Simulation
• Spatio-temporal model
• Applied Statistics
• Biostatistics

Statement dc:rights

• <p>In Copyright. URI: <a href="http://rightsstatements.org/vocab/InC/1.0/">http://rightsstatements.org/vocab/InC/1.0/</a> This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).</p>

Identifier

9781392268087

OAI identifier oai:identifier

oai:digitalcommons.odu.edu:mathstat_etds-1051