Asymptotic properties of the maximum pseudo-likelihood estimator for stationary Gibbs point processes including the Lennard-Jones model

This paper presents asymptotic properties of the maximum pseudo-likelihood estimator of a vector \Vect{\theta} parameterizing a stationary Gibbs point process. Sufficient conditions, expressed in terms of the local energy function defining a Gibbs point process, to establish strong consistency and asymptotic normality results of this estimator depending on a single realization, are presented.These results are general enough to no longer require the local stability and the linearity in terms of the parameters of the local energy function. We consider characteristic examples of such models, the Lennard-Jones and the finite range Lennard-Jones models. We show that the different assumptions ensuring the consistency are satisfied for both models whereas the assumptions ensuring the asymptotic normality are fulfilled only for the finite range Lennard-Jones model

Maximum pseudo-likelihood estimator for nearest-neighbours Gibbs point processes

This paper is devoted to the estimation of a vector parametrizing an energy function associated to some "Nearest-Neighbours" Gibbs point process, via the pseudo-likelihood method. We present some convergence results concerning this estimator, that is strong consistency and asymptotic normality, when only a single realization is observed. Sufficient conditions are expressed in terms of the local energy function and are verified on some examples.Comment: 29 pages - 2 figure

Normalized information-based divergences

This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their main characteristic is that they combine a complexity term and the mutual information. We then introduce the notion of (normalized) information-based divergence, propose several examples and discuss their mathematical properties in particular in some prediction framework.Comment: 36 page

Maximum pseudolikelihood estimator for exponential family models of marked Gibbs point processes

This paper is devoted to the estimation of a vector $\bm {\theta}$ 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.Comment: Published in at http://dx.doi.org/10.1214/07-EJS160 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic properties of the maximum pseudolikelihood estimator for stationary Gibbs point processes including the LennardJones model

Abstract: This paper presents asymptotic properties of the maximum pseudo-likelihood estimator of a vector parameterizing a stationary Gibbs point process. Sufficient conditions, expressed in terms of the local energy function defining a Gibbs point process, to establish strong consistency and asymptotic normality results of this estimator depending on a single realization, are presented. These results are general enough to no longer require the local stability and the linearity in terms of the parameters of the local energy function. We consider characteristic examples of such models, the Lennard-Jones and the finite range Lennard-Jones models. We show that the different assumptions ensuring the consistency are satisfied for both models whereas the assumptions ensuring the asymptotic normality are fulfilled only for the finite range Lennard-Jones model

asympTest: an R package for performing parametric statistical tests and confidence intervals based on the central limit theorem

This paper describes an R package implementing large sample tests and confidence intervals (based on the central limit theorem) for various parameters. The one and two sample mean and variance contexts are considered. The statistics for all the tests are expressed in the same form, which facilitates their presentation. In the variance parameter cases, the asymptotic robustness of the classical tests depends on the departure of the data distribution from normality measured in terms of the kurtosis of the distribution

R-local Delaunay inhibition model

Let us consider the local specification system of Gibbs point process with inhib ition pairwise interaction acting on some Delaunay subgraph specifically not con taining the edges of Delaunay triangles with circumscribed circle of radius grea ter than some fixed positive real value $R$. Even if we think that there exists at least a stationary Gibbs state associated to such system, we do not know yet how to prove it mainly due to some uncontrolled "negative" contribution in the expression of the local energy needed to insert any number of points in some large enough empty region of the space. This is solved by introducing some subgraph, called the $R$-local Delaunay graph, which is a slight but tailored modification of the previous one. This kind of model does not inherit the local stability property but satisfies s ome new extension called $R$-local stability. This weakened property combined with the local property provides the existence o f Gibbs state.Comment: soumis \`{a} Journal of Statistical Physics 27 page

Une vie polyamoureuse entre R et Julia

International audienceLe langage julia partage avec le langage R les caract´eristiques comme l’indexation des tableauxcommen¸cant `a 1, le (multiple) dispatching, la metaprogramming et son syst`eme unique de gestion deslibrairies (paquets). A la diff´erence de R, julia proposant une compilation JIT (Just In Time) estintrins`equement plus performant que le langage R, r´etablissant au passage l’utilisation des bouclesfor comme c’est le cas pour les langages compil´es. De par sa jeunesse (un peu plus de 10 ans),julia reste toutefois un langage en devenir surtout au niveau du d´eveloppement de son ´ecosyst`emede paquets. Pour toutes ces raisons, le langage julia peut ˆetre vu comme un digne successeur dulangage R. Dans cette pr´esentation, nous proposons le paquet R, nomm´e jl4R, dont l’objectif avou´eest de t´el´eguider depuis R des paquets julia. L’esprit du paquet est principalement d’imaginer lejulia comme un remplacement de Rcpp et ainsi de proposer des paquets R de type wrapper depaquet julia

VAM

R package dealing with Virtual Age Model

Computing wedge probabilities

A new formula for the probability that a standard Brownian motion stays between two linear boundaries is proved. A simple algorithm is deduced. Uniform precision estimates are computed. Different implementations have been made available online as R packages