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The immense progress in data collection and storage capacities have yielded rather complex, challenging spatial event-type data, where each event location is augmented by a non-simple mark. Despite the growing interest in analysing such complex event patterns, the methodology for such analysis is not embedded well in the literature. In particular, the literature lacks statistical methods to analyse marks which are characterised by an inherent relational structure, i.e.\ where the mark is graph-valued. Motivated by epidermal nerve fibre data, we introduce different mark summary characteristics, which investigate the average variation or association between pairs of graph-valued marks, and apply some of the methods to the nerve data., Comment: submitted for publication

Many natural systems are observed as point patterns in time, space, or space and time. Examples include plant and cellular systems, animal colonies, earthquakes, and wildfires. In practice the locations of the points are not always observed correctly. However, in the point process literature, there has been relatively scant attention paid to the issue of errors in the location of points. In this paper, we discuss how the observed point pattern may deviate from the actual point pattern and review methods and models that exist to handle such deviations. The discussion is supplemented with several scientific illustrations.

Diabetic neuropathy is a disorder characterized by impaired nerve function and reduction of the number of epidermal nerve fibers per epidermal surface. Additionally, as neuropathy related nerve fiber loss and regrowth progresses over time, the two-dimensional spatial arrangement of the nerves becomes more clustered. These observations suggest that with development of neuropathy, the spatial pattern of diminished skin innervation is defined by a thinning process which remains incompletely characterized. We regard samples obtained from healthy controls and subjects suffering from diabetic neuropathy as realisations of planar point processes consisting of nerve entry points and nerve endings, and propose point process models based on spatial thinning to describe the change as neuropathy advances. Initially, the hypothesis that the nerve removal occurs completely at random is tested using independent random thinning of healthy patterns. Then, a dependent parametric thinning model that favors the removal of isolated nerve trees is proposed. Approximate Bayesian computation is used to infer the distribution of the model parameters, and the goodness-of-fit of the models is evaluated using both non-spatial and spatial summary statistics. Our findings suggest that the nerve mortality process changes behaviour as neuropathy advances.

We propose a hierarchical log Gaussian Cox process (LGCP) for point patterns, where a set of points x affects another set of points y but not vice versa. We use the model to investigate the effect of large trees to the locations of seedlings. In the model, every point in x has a parametric influence kernel or signal, which together form an influence field. Conditionally on the parameters, the influence field acts as a spatial covariate in the intensity of the model, and the intensity itself is a non-linear function of the parameters. Points outside the observation window may affect the influence field inside the window. We propose an edge correction to account for this missing data. The parameters of the model are estimated in a Bayesian framework using Markov chain Monte Carlo (MCMC) where a Laplace approximation is used for the Gaussian field of the LGCP model. The proposed model is used to analyze the effect of large trees on the success of regeneration in uneven-aged forest stands in Finland., Comment: 28 pages, 9 figures

The aim of the paper is to construct spatial models for the activation of sweat glands for healthy subjects and subjects suffering from peripheral neuropathy by using videos of sweating recorded from the subjects. The sweat patterns are regarded as realizations of spatial point processes and two point process models for the sweat gland activation and two methods for inference are proposed. Several image analysis steps are needed to extract the point patterns from the videos and some incorrectly identified sweat gland locations may be present in the data. To take into account the errors we either include an error term in the point process model or use an estimation procedure that is robust with respect to the errors., Comment: 27 pages, 12 figures

A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this paper, we give an overview of nonparametric methods for anisotropy analysis of (stationary) point patterns in $\mathbf{R}^2$ and $\mathbf{R}^3$. We discuss methods based on nearest neighbour and second order summary statistics as well as spectral and wavelet analysis. All techniques are illustrated on both a clustered and a regular example. Finally, we discuss methods for testing for isotropy as well as for estimating preferred directions in a point pattern., Comment: Submitted to Spatial Statistics -journal's special issue of the Spatial Statistics 2017 conference

How do people look at art? Are there any differences between how experienced and inexperienced art viewers look at a painting? We approach these questions by analyzing and modeling eye movement data from a cognitive art research experiment, where the eye movements of twenty test subjects, ten experienced and ten inexperienced art viewers, were recorded while they were looking at paintings. Eye movements consist of stops of the gaze as well as jumps between the stops. Hence, the observed gaze stop locations can be thought as a spatial point pattern, which can be modeled by a spatio-temporal point process. We introduce some statistical tools to analyze the spatio-temporal eye movement data, and compare the eye movements of experienced and inexperienced art viewers. In addition, we develop a stochastic model, which is rather simple but fits quite well to the eye movement data, to further investigate the differences between the two groups through functional summary statistics., Comment: 29 pages, 15 figures