Jean-Noël Bacro

Estimation of spatial max-stable models using threshold exceedances

Parametric inference for spatial max-stable processes is difficult since the related likelihoods are unavailable. A composite likelihood approach based on the bivariate distribution of block maxima has been recently proposed. However modeling block maxima is a wasteful approach provided that other information is available. Moreover an approach based on block maxima, typically annual, is unable to take into account the fact that maxima occur or not simultaneously. If time series of, say, daily data are available, then estimation procedures based on exceedances of a high threshold could mitigate such problems. We focus on two approaches for composing likelihoods based on pairs of exceedances. The first one comes from the tail approximation for bivariate distribution proposed by Ledford and Tawn (Biometrika 83:169–187, 1996) when both pairs of observations exceed the fixed threshold. The second one uses the bivariate extension (Rootzén and Tajvidi in Bernoulli 12:917–930, 2006) of the generalized Pareto distribution which allows to model exceedances when at least one of the components is over the threshold. The two approaches are compared through a simulation study where both processes in a domain of attraction of a max-stable process and max-stable processes are successively considered as time replications, according to different degrees of spatial dependency. Results put forward how the nature of the time replications influences the bias of estimations and highlight the choice of each approach regarding to the strength of the spatial dependencies and the threshold choice.

ESTIMATION OF AN AGE DISTRIBUTION WITH ITS CONFIDENCE INTERVALS USING AN ITERATIVE BAYESIAN PROCEDURE AND A BOOTSTRAP SAMPLING APPROACH

An iterative Bayesian estimation procedure is used in order to explore two classes of models pertaining to the universe of preindustrial demographic mortality. One model is for “attritional” mortality and the other for “catastrophic” mortality. The estimation procedure first extracts the model which best fits the data representing the distribution of age indicators in a cemetery. Then, using the anthropological reference sample of the age indicator, a bootstrap sampling technique determines the confidence interval for the estimation. Through simulations, we show that if the cemetery belongs to the class of the models explored, i.e. if the model is true, then the result is excellent for an age/indicator correlation level of about r=0.9

A Hierarchical Bayesian Model for Spatial Prediction of Multivariate Non-Gaussian Random Fields

As most georeferenced data sets are multivariate and concern variables of different types, spatial mapping methods must be able to deal with such data. The main difficulties are the prediction of non-Gaussian variables and the modeling of the dependence between processes. The aim of this article is to present a new hierarchical Bayesian approach that permits simultaneous modeling of dependent Gaussian, count, and ordinal spatial fields. This approach is based on spatial generalized linear mixed models. We use a moving average approach to model the spatial dependence between the processes. The method is first validated through a simulation study. We show that the multivariate model has better predictive abilities than the univariate one. Then the multivariate spatial hierarchical model is applied to a real data set collected in French Guiana to predict topsoil patterns.

Alcohol and atherosclerotic vascular disease risk factors in French men: relationships are linear, J-shaped, and U-shaped.

BACKGROUND Although it is well admitted that alcohol displays a U-shaped relationship with atherosclerotic vascular disease, individual relationships between alcohol and atherosclerosis risk factors may be different and have not been determined precisely for several of them. METHODS A cross-sectional study within the SU.VI.MAX French cohort study was performed to assess the curve of potential relationships between alcohol and atherosclerosis risk factors in 2126 healthy men. Mean daily alcohol intake was derived from 37 alcoholic beverages in twelve 24-hr dietary recalls. Logistic models were adjusted for age. RESULTS Apolipoprotein B (ApoB), fasting glucose, body mass index, waist-to-hip ratio, and waist circumference displayed a linear relationship with alcohol. The odds ratios and 95% confidence intervals associated with abnormal values of the markers for the highest quintile of alcohol intake were 1.45 (1.06-1.97) for ApoB, 1.98 (1.40-2.80) for fasting glucose, and 1.74 (1.30-2.34) for body mass index. An inverse J-shaped relationship was assumed for ApoA1 and ApoB/ApoA1 ratio, whereas a U-shaped relationship was observed for serum triglycerides and mixed hyperlipidemia. Only the highest quintile of alcohol was associated with hypertension, although the test for linearity was also significant. No association was observed for Lp(a) or homocysteine. Associations were unmodified by further adjustment for carbohydrates, fiber, lipids, tobacco, or exercise. CONCLUSIONS The aggregate of the disparate alcohol risk factor relationships suggests probable net benefit at 15 to 25 g of alcohol/day.

Statistical Inference for the Generalized Pareto Distribution: Maximum Likelihood Revisited

The maximum likelihood system of equations for the shape and scale parameters ξ and β of a generalized Pareto distribution is summarized through a single equation h x (ρ) = 0 where x designates the n-sample of realizations and . The study of the function h x (ρ) in the neighborhood of 0 puts forward a simple statistic S(x) only based on the first two empirical moments which is independent from β. This statistic allows to build an immediate and easy to use statistical test for ξ. The power of this test appears as quite similar to the one of already known test procedures which are much more difficult to use in practice. Moreover, the maximum likelihood solution of h x (ρ) = 0, say ρˆ, and S(x) both have the same sign. This property allows us to propose a controlled use of standard optimization algorithms for characterizing ρˆ, and as a consequence, the maximum likelihood estimations of ξ and β, without any risk of convergence failure or aberrant solution.

A Review on Spatial Extreme Modelling

In this chapter we review recent advances in modelling spatial extremes. After a brief illustration of the extreme value theory for univariate and multivariate values, we concentrate on spatial max-stable processes. Statistical inference and simulation for these processes are subject of a close examination. Max-stable processes are also contrasted with spatial hierarchical models. The review ends with summarizing some open problems.

Estimating and testing zones of abrupt change for spatial data

We propose a method for detecting the zones where a variable irregularly sampled in the plane changes abruptly. Our general model is that under the null hypothesis the variable is the realisation of a stationary Gaussian process with constant expectation. The alternative is that the mean function presents abrupt changes. We define potential Zones of Abrupt Change (ZACs) by the points where the gradient, estimated under the null hypothesis, exceeds a determined threshold. We then design a global test to assess the global significance of the potential ZACs, an issue missing in all existing methods. The theory that links the threshold and the global level is based on asymptotic distributions of excursion sets of non-stationary χ2 fields for which we provide new results. The method is evaluated by a simulation study and applied to a soil data set in the context of precision agriculture.

Hierarchical Bayesian Model for Gaussian, Poisson and Ordinal Random Fields

As most georeferenced data sets are multivariate and concern variables of different kinds, spatial mapping methods must be able to deal with such data. The main difficulties are the prediction of non Gaussian variables and the modelling of the dependence between processes. The aim of this paper is to propose a new approach that permits simultaneous modelling of Gaussian, count and ordinal spatial processes. We consider a hierarchical model implemented within a Bayesian framework. The method used for Gaussian and count variables is based on the generalized linear mixed models. Ordinal variable is taken into account through a generalization of the ordinal probit model. We use a moving average approach to model the spatial dependence between the processes. The proposed model is applied to pedological data collected in French Guiana.

Ultrastructural localization and distribution of Nardilysin in mammalian male germ cells

BackgroundNRD convertase, also termed Nardilysin, is a Zn++ metalloendopeptidase that specifically cleaves the N-terminus of arginine and lysine residues into dibasic moieties. Although this enzyme was found located within the testis, its function in male reproduction is largely unknown. In addition, the precise distribution of this enzyme within germ cells remains to be determined.MethodsTo answer these questions, we developed an immuno-gold electron microscopy analysis to detect Nardilysin at ultrastructural level in mice. In addition, we performed a quantitative analysis of these gold particles to statistically estimate the distribution of Nardilysin in the different subcellular compartments of differentiating late spermatids/spermatozoa.ResultsExpression of Nardilysin in wild-type mice was restricted to germ cells and markedly increased during the last steps of spermiogenesis. In elongated spermatids, we found the enzyme mainly localized in the cytoplasm, more precisely associated with two microtubular structures, the manchette and the axoneme. No labelling was detected over the membranous organelles of the spermatids. To test whether this localization is dependent of the functional microtubules organization of the flagella, we analysed the localization into a specific mouse mutant ebo/ebo (ébouriffé) known to be sterile due to an impairment of the final organization of the flagellum. In the ebo/ebo, the enzyme was still localized over the microtubules of the axoneme and over the isolated cytoplasmic microtubules doublets. Quantification of gold particles in wild-type and mutant flagella revealed the specific association of the enzyme within the microtubular area of the axoneme.ConclusionsThe strong and specific accumulation of Nardilysin in the manchette and axoneme suggests that the enzyme probably contributes either to the establishment of these specific microtubular structures and/or to their functional properties.RésuméObjectifsLa NRD convertase aussi appelée Nardilysine, une Zn++ metalloendopeptidase qui clive spécifiquement dans la région N terminale des résidus arginine et lysine des sites dibasiques, est impliquée dans la transformation/maturation des proprotéines. Le but de cette étude est de localiser cette enzyme durant la spermiogénèse afin de comprendre son rôle au cours de la maturation des spermatides.MéthodesLa Nardilysine est révélée par immunohistochimie au niveau ultrastructural chez des souris contrôles fertiles et chez un mutant stérile (ébouriffé : ebo/ebo). Des analyses quantitatives sont effectuées par comptage des grains d’or colloïdal qui permettent de détecter la localisation spécifique de l’enzyme au cours de la croissance des spermatides dans des régions particulières.RésultatsL’expression de la Nardilysine chez les souris sauvages et stériles ebo/ebo est limitée aux cellules germinales avec une augmentation significative dans les étapes ultimes de la spermiogénèse. L’enzyme est fortement exprimée dans le cytoplasme des spermatides allongées et dans les structures microtubulaires, la manchette et le flagelle. Aucun marquage n’est observé au niveau des organites cellulaires des spermatides. Chez le mutant ebo/ebo, dont le flagelle est anormal, l’enzyme est toujours présente sur les doublets de microtubules du flagelle. La quantification des particules d’or chez la souris sauvage et chez le mutant révèle une association spécifique de l’enzyme avec les microtubules du flagelle.ConclusionsL’accumulation spécifique de la Nardilysine au niveau de la manchette et du flagelle suggère que cette enzyme pourrait contribuer à l’établissement de ces structures microtubulaires particulières et/ou à leurs propriétés fonctionnelles.