Envelope tests are a popular tool in spatial statistics, where they are used in goodness-of-fit testing. These tests graphically compare an empirical function $T(r)$ with its simulated counterparts from the null model. However, the type I error probability $\alpha$ is conventionally controlled for a fixed distance $r$ only, whereas the functions are inspected on an interval of distances $I$. In this study, we propose two approaches related to Barnard's Monte Carlo test for building global envelope tests on $I$:(1) ordering the empirical and simulated functions based on their $r$-wise ranks among each other, and (2) the construction of envelopes for a deviation test. These new tests allow the a priori selection of the global $\alpha$ and they yield $p$-values. We illustrate these tests using simulated and real point pattern data

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Breakthroughs in imaging of skin tissue reveal new details on the distribution of nerve fibers in the epidermis. Preliminary neurologic studies indicate qualitative differences in the spatial patterns of nerve fibers based on pathophysiologic conditions in the subjects. Of particular interest is the evolution of spatial patterns observed in the progression of diabetic neuropathy. It appears that the spatial distribution of nerve fibers becomes more 'clustered' as neuropathy advances, suggesting the possibility of diagnostic prediction based on patterns observed in skin biopsies. We consider two approaches to establish statistical inference relating to this observation. First, we view the set of locations where the nerves enter the epidermis from the dermis as a realization of a spatial point process. Secondly, we treat the set of fibers as a realization of a planar fiber process. In both cases, we use estimated second-order properties of the observed data patterns to describe the degree and scale of clustering observed in the microscope images of blister biopsies. We illustrate the methods using confocal microscopy blister images taken from the thigh of one normal (disease-free) individual and two images each taken from the thighs of subjects with mild, moderate, and severe diabetes and report measurable differences in the spatial patterns of nerve entry points/fibers associated with disease status.

A problem in the single-scan setup of terrestrial laser scanning is that some trees are shaded by others and therefore not detected in the scan. A basic estimator for forest characteristics such as tree density or basal area is based on the visible area of a scanner. However, simply compensating for nondetection by the visible area may result in considerable bias even in Poisson forests, especially if the detection of a tree depends on its size. We propose a new estimator that is a generalization of the visible area based estimator. Most importantly, the new estimator allows different detection rules; for example, full or partial visibility of a tree can be required for detection. By a simulation study, it is shown to work adequately in different types of simulated and empirical forests with different detection rules.

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