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Weighted Cross J-Function and Its Application to African Avian Flu Data


It is common to use geostatistical techniques to analyze epidemiological data. However, we might gain further insight by viewing these types of data as a point pattern due to the spatial nature of the dataset which would allow us to use the spatial information of each point and apply point process techniques. Point process techniques are applied to the avian influenza virus data, and a summary statistic called the weighted cross J-function is proposed. The ordinary cross J-function is extended to a weighted version by incorporating weights to account for inhomogeneity because this dataset appears to exhibit non-constant intensity. Unlike the ordinary cross J-function, the weighted cross J-function takes into account the varying background rate of the point process by incorporating weights for each point in the point patterns. The advantage of the weighted cross J -function is that it is used to measure the interaction between events in two point processes and to detect clustering or inhibition between them, in order to recognize where spatial interaction appears most prevalent. We introduce the weighted cross J-function, discuss its properties, demonstrate it with simulations and show its application to the African Avian Flu dataset.

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