Resample-smoothing of Voronoi intensity estimators

Voronoi estimators are non-parametric and adaptive estimators of the intensity of a point process. The intensity estimate at a given location is equal to the reciprocal of the size of the Voronoi/Dirichlet cell containing that location. Their major drawback is that they tend to paradoxically under-smooth the data in regions where the point density of the observed point pattern is high, and over-smooth where the point density is low. To remedy this behaviour, we propose to apply an additional smoothing operation to the Voronoi estimator, based on resampling the point pattern by independent random thinning. Through a simulation study we show that our resample-smoothing technique improves the estimation substantially. In addition, we study statistical properties such as unbiasedness and variance, and propose a rule-of-thumb and a data-driven cross-validation approach to choose the amount of smoothing to apply. Finally we apply our proposed intensity estimation scheme to two datasets: locations of pine saplings (planar point pattern) and motor vehicle traffic accidents (linear network point pattern)

Statistical disclosure control when publishing on thematic maps

The spatial distribution of a variable, such as the energy consumption per company, is usually plotted by colouring regions of the study area according to an underlying table which is already protected from disclosing sensitive information. The result is often heavily influenced by the shape and size of the regions. In this paper, we are interested in producing a continuous plot of the variable directly from microdata and we protect it by adding random noise. We consider a simple attacker scenario and develop an appropriate sensitivity rule that can be used to determine the amount of noise needed to protect the plot from disclosing private information

A statistical approach to estimating the strength of cell-cell interactions under the differential adhesion hypothesis

International audienceBACKGROUND: The Differential Adhesion Hypothesis (DAH) is a theory of the organization of cells within a tissue which has been validated by several biological experiments and tested against several alternative computational models. RESULTS: In this study, a statistical approach was developed for the estimation of the strength of adhesion, incorporating earlier discrete lattice models into a continuous marked point process framework. This framework allows to describe an ergodic Markov Chain Monte Carlo algorithm that can simulate the model and reproduce empirical biological patterns. The estimation procedure, based on a pseudo-likelihood approximation, is validated with simulations, and a brief application to medulloblastoma stained by beta-catenin markers is given. CONCLUSION: Our model includes the strength of cell-cell adhesion as a statistical parameter. The estimation procedure for this parameter is consistent with experimental data and would be useful for high-throughput cancer studies

Book review: Statistical analysis and modelling of spatial point processes

NO ABSTRAC

Depth map calculation for a variable number of moving objects using Markov sequential object processes

We advocate the use of Markov sequential object processes for tracking a variable number of moving objects through video frames with a view towards depth calculation. A regression model based on a sequential object process quantifies goodness of fit; regularization terms are incorporated to control within and between frame object interactions. We construct a Markov chain Monte Carlo method for finding the optimal tracks and associated depths and illustrate the approach on a synthetic data set as well as a sport sequence

On estimation of the intensity function of a point process

In this paper we review techniques for estimating the intensity function of a spatial point process. We present a unified framework of mass preserving general weight function estimators that encompasses both kernel and tessellation based estimators. We give explicit expressions for the first two moments of these estimators in terms of their product densities, and pay special attention to Poisson processes

Size-biased random closed sets

We indicate how granulometries may be useful in the analysis of random sets. After defining a size distribution function which may be used as a summary statistic in exploratory data analysis, we propose a Hanisch-type estimator and construct new Markov random set models which favour certain sizes above others. The models are illustrated by simulated realisations