Date of Award

Spring 5-2021

Degree Type

Thesis

Degree Name

M.S.

Degree Program

Mathematics

Department

Mathematics

Major Professor

Xueyan Liu

Second Advisor

Linxiong Li

Third Advisor

Tumulesh Solanky

Abstract

Spatial point pattern analysis investigates the localizations of random events in a defined spatial space usually conveyed in the form of images. Spatial distribution of two types of events observed in these images reflects their underlying interactions, which is the focus of co-localization analysis in spatial statistics. Malkusch et al. (Malkusch, et al., 2012) recently proposed the Coordinate-based Co-localization (CBC) method for co-localization analysis. However, the method did not incorporate edge corrections for point proportions and ignored their correlations over nested incremental observational regions. Hence, it yields false positive results for even complete spatial random distributions. In this research, we propose the new K(r) function Coordinate-based Colocalization (KCBC) method to quantify co-localization of two species by utilizing local bivariate Ripley's K and Pearson’s Correlation Coefficient. Simulation studies are conducted to demonstrate the unbiasedness of the new method. An application to real life data was provided to illustrate its applicability.

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The University of New Orleans and its agents retain the non-exclusive license to archive and make accessible this dissertation or thesis in whole or in part in all forms of media, now or hereafter known. The author retains all other ownership rights to the copyright of the thesis or dissertation.

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