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

Identification d'un gène majeur influençant le taux d'ovulation en race ovine Lacaune

Chez les ovins, la prolificité est un critère important sélectionné pour la production d'agneaux. En race Lacaune, une mutation autosomale (FecL, chromosome 11 ovin) qui augmente le taux d'ovulation et donc la prolificité des brebis a été mise en évidence. Les objectifs de cette thèse étaient d'une part, la localisation fine et le clonage positionnel de FecL et d'autre part, la caractérisation des conséquences physiologiques de la mutation. Une centaine de marqueurs génétiques ont été développés à partir des séquences disponibles, puis par séquençage haut débit. Le génotypage de familles expérimentales a permis de réduire le locus FecL à une région de 190 kb qui comprend deux gènes, IGF2BP1 et B4GALNT2. Différents éléments, tels que la présence d'un SNP dans un intron du gène B4GALNT2 en total déséquilibre de liaison avec la mutation et une très forte surexpression des ARNm de B4GALNT2 dans les ovaires des brebis mutées, désignent ce gène comme le gène FecL. Au niveau physiologique, les brebis mutées sont caractérisées par un plus grand nombre de follicules matures et une expression augmentée du récepteur à FSH dans l'ovaire, une concentration plus élevée en œstradiol circulant qui entraine une accélération de la pulsatilité et une décharge préovulatoire de LH plus précoce. L'hypothèse retenue serait une action de FecL sur le phénomène de sélection des follicules conduisant à une augmentation du taux d'ovulation. Jusqu'à présent, dans l'espèce ovine, toutes les mutations identifiées influençant le taux d'ovulation concernent le système TGFß. Cette thèse met en évidence une nouvelle voie de régulation de la fonction ovarienne et du taux d'ovulation chez la brebis.In sheep, prolificacy is a important criteria selected in lamb production. In the Lacaune breed, an autosomal mutation (FecL, chromosome 11) increasing ovulation rate and therefore ewes prolificacy has been evidenced. The goals of this work were on one hand, the fine mapping of FecL, and on the other hand, the endocrine characterization of the reproductive axis in highly prolific Lacaune sheep. About one hundred markers have been developed first from available sequences then from high-throughput sequencing. Genotyping of experimental families led to a locus of 190kb containing FecL, encompassing two genes, IGF2BP1 and B4GALNT2. The presence of a SNP completely associated with the mutation localized in an intron of B4GALNT2 gene and the over expression of B4GALNT2 mRNA in mutated ovaries led us to consider this gene as the FecL gene. Physiologically, the mutated ewes have a greater number of mature follicles and an over expression of the FSH receptor in ovary, a higher plasmatic oestradiol concentration leading to a higher LH pulsatility and then a precocious LH preovulatory surge. One hypothesis could be that FecL influences follicles selection leading to an increased ovulation rate. Until now, in sheep breed, all the identified mutations influencing ovulation rate belong to the TGFß system. This work evidences a new regulatory pathway of the ovary function and ovulation rate in ewes

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

DynPeak : An algorithm for pulse detection and frequency analysis in hormonal time series

The endocrine control of the reproductive function is often studied from the analysis of luteinizing hormone (LH) pulsatile secretion by the pituitary gland. Whereas measurements in the cavernous sinus cumulate anatomical and technical difficulties, LH levels can be easily assessed from jugular blood. However, plasma levels result from a convolution process due to clearance effects when LH enters the general circulation. Simultaneous measurements comparing LH levels in the cavernous sinus and jugular blood have revealed clear differences in the pulse shape, the amplitude and the baseline. Besides, experimental sampling occurs at a relatively low frequency (typically every 10 min) with respect to LH highest frequency release (one pulse per hour) and the resulting LH measurements are noised by both experimental and assay errors. As a result, the pattern of plasma LH may be not so clearly pulsatile. Yet, reliable information on the InterPulse Intervals (IPI) is a prerequisite to study precisely the steroid feedback exerted on the pituitary level. Hence, there is a real need for robust IPI detection algorithms. In this article, we present an algorithm for the monitoring of LH pulse frequency, basing ourselves both on the available endocrinological knowledge on LH pulse (shape and duration with respect to the frequency regime) and synthetic LH data generated by a simple model. We make use of synthetic data to make clear some basic notions underlying our algorithmic choices. We focus on explaining how the process of sampling affects drastically the original pattern of secretion, and especially the amplitude of the detectable pulses. We then describe the algorithm in details and perform it on different sets of both synthetic and experimental LH time series. We further comment on how to diagnose possible outliers from the series of IPIs which is the main output of the algorithm.Comment: Nombre de pages : 35 ; Nombre de figures : 16 ; Nombre de tableaux :

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