We propose a computationally efficient technique, based on logistic regression, for fitting Gibbs point process models to spatial point pattern data. The score of the logistic regression is an unbiased estimating function and is closely related to the pseudolikelihood score. Implementation of our technique does not require numerical quadrature, and thus avoids a source of bias inherent in other methods. For stationary processes, we prove that the parameter estimator is strongly consistent and asymptotically normal, and propose a variance estimator. We demonstrate the efficiency and practicability of the method on a real dataset and in a simulation study.

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: We present a non exhaustive bibliographical and comparative study of the problem of simulation and identification of the fractional Brownian motion. The discussed implementation is realized within the software S-plus 3.4. A few simulations illustrate this work. Furthermore, we propose a test based on the asymptotic behavior of a self-similarity parameter's estimator to explore the quality of different generators. This procedure, easily computable, allows us to extract an efficient method of simulation. In the Appendix are described the S-plus scripts related to simulation and identification methods of the fBm.

This paper is devoted to the estimation of a vector θ parametrizing an energy function of a Gibbs point process, via the maximum pseudolikelihood method. Strong consistency and asymptotic normality results of this estimator depending on a single realization are presented. In the framework of exponential family models, sufficient conditions are expressed in terms of the local energy function and are verified on a wide variety of examples.

Figure 1: Given a reference arrangement composed of vector elements (top left), our analysis scheme divides the raw element set into appearance categories (bottom left). Spatial interactions based on appearance can be learned by statistical modeling and exploited to yield visually similar arrangements (right). AbstractWe present a technique for the analysis and re-synthesis of 2D arrangements of stroke-based vector elements. The capture of an artist's style by the sole posterior analysis of his/her achieved drawing poses a formidable challenge. Such by-example techniques could become one of the most intuitive tools for users to alleviate creation process efforts. Here, we propose to tackle this issue from a statistical point of view and take specific care of accounting for information usually overlooked in previous research, namely the elements' very appearance. Composed of curve-like strokes, we describe elements by a concise set of perceptually relevant features. After detecting appearance dominant traits, we can generate new arrangements that respect the captured appearance-related spatial statistics using multitype point processes. Our method faithfully reproduces visually similar arrangements and relies on neither heuristics nor post-processes to ensure statistical correctness.