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Book Summary:
Estimation of the intensity function is widely used in spatial data analysis. The intensity function refers to the average number of events expected per unit area and therefore, computing the ratio of intensities is useful for relative risk analyses. Ratios of intensity functions for two spatial point processes (e.g., cases and controls) over the same study area also serve as local measures of relative risk, however existing approaches for interval estimation are pointwise rather than simultaneous. We develop and contrast methods (and associated asymptotic results) providing simultaneous confidence intervals for smoothly varying functions in space, deriving and using correlations between local test statistics. Specifically, we derive the theoretical correlation between tests from different locations in order to calculate the effective number of independent tests yielding a Bonferroni-type adjustment for multiple tests. Second, we also use empirical estimates of the autocorrelation function to evaluate an empirical version of the same approach. Third, we adjust test results via false-discovery rate (FDR) mechanisms by relaxing the usual independence assumptions associated with FDR approaches. We use the developed methodology to conduct a spatial analysis of sea turtle nesting in Palm Beach County, Florida. Specifically, we estimate the intensity of sea turtle nesting emergences (number of nesting emergences per unit length of beach) as a function of beach location, and compare intensities of nesting emergences between years 1997 and 2000. In addition to inference for intensity functions, we also consider second-order summaries of spatial point processes and develop an average K function to quantify the spatial scale of clustering observed in single and multiple medical images in order to compare spatial patterns between normal and diseased patients. We apply the approach to images of epidermal nerve fibers in patients with and without small fiber sensory neuropathy, quantifying an observed increase in clustering for diseased patients. |
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