Wave-height hazard analysis in Eastern Coast of Spain : Bayesian approach using generalized Pareto distribution

Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated using data from the Mediterranean coast of Spain, where the last years have been extremely disastrous. Thus, it is possible to compare the hazard assessment based on data previous to those years with the analysis including them. With our approach, no significant change is detected when the statistical uncertainty is taken into account. The hazard analysis is carried out with a standard model. Time-occurrence of events is assumed Poisson distributed. The wave-height of each event is modelled as a random variable which upper tail follows a Generalized Pareto Distribution (GPD). Moreover, wave-heights are assumed independent from event to event and also independent of their occurrence in time. A threshold for excesses is assessed empirically. The other three parameters (Poisson rate, shape and scale parameters of GPD) are jointly estimated using Bayes' theorem. Prior distribution accounts for physical features of ocean waves in the Mediterranean sea and experience with these phenomena. Posterior distribution of the parameters allows to obtain posterior distributions of other derived parameters like occurrence probabilities and return periods. Predictives are also available. Computations are carried out using the program BGPE v2.0

Spectral energy distribution of the gamma-ray microquasar LS 5039

The microquasar LS 5039 has recently been detected as a source of very high energy (VHE) $\gamma$-rays. This detection, that confirms the previously proposed association of LS 5039 with the EGRET source 3EG~J1824$-$1514, makes of LS 5039 a special system with observational data covering nearly all the electromagnetic spectrum. In order to reproduce the observed spectrum of LS 5039, from radio to VHE $\gamma$-rays, we have applied a cold matter dominated jet model that takes into account accretion variability, the jet magnetic field, particle acceleration, adiabatic and radiative losses, microscopic energy conservation in the jet, and pair creation and absorption due to the external photon fields, as well as the emission from the first generation of secondaries. The radiative processes taken into account are synchrotron, relativistic Bremsstrahlung and inverse Compton (IC). The model is based on a scenario that has been characterized with recent observational results, concerning the orbital parameters, the orbital variability at X-rays and the nature of the compact object. The computed spectral energy distribution (SED) shows a good agreement with the available observational data.

Approximation de la distribution a posteriori d'un modèle Gamma-Poisson hiérarchique à effets mixtes

La méthode que nous présentons pour modéliser des données dites de "comptage" ou données de Poisson est basée sur la procédure nommée Modélisation multi-niveau et interactive de la régression de Poisson (PRIMM) développée par Christiansen et Morris (1997). Dans la méthode PRIMM, la régression de Poisson ne comprend que des effets fixes tandis que notre modèle intègre en plus des effets aléatoires. De même que Christiansen et Morris (1997), le modèle étudié consiste à faire de l'inférence basée sur des approximations analytiques des distributions a posteriori des paramètres, évitant ainsi d'utiliser des méthodes computationnelles comme les méthodes de Monte Carlo par chaînes de Markov (MCMC). Les approximations sont basées sur la méthode de Laplace et la théorie asymptotique liée à l'approximation normale pour les lois a posteriori. L'estimation des paramètres de la régression de Poisson est faite par la maximisation de leur densité a posteriori via l'algorithme de Newton-Raphson. Cette étude détermine également les deux premiers moments a posteriori des paramètres de la loi de Poisson dont la distribution a posteriori de chacun d'eux est approximativement une loi gamma. Des applications sur deux exemples de données ont permis de vérifier que ce modèle peut être considéré dans une certaine mesure comme une généralisation de la méthode PRIMM. En effet, le modèle s'applique aussi bien aux données de Poisson non stratifiées qu'aux données stratifiées; et dans ce dernier cas, il comporte non seulement des effets fixes mais aussi des effets aléatoires liés aux strates. Enfin, le modèle est appliqué aux données relatives à plusieurs types d'effets indésirables observés chez les participants d'un essai clinique impliquant un vaccin quadrivalent contre la rougeole, les oreillons, la rub\'eole et la varicelle. La régression de Poisson comprend l'effet fixe correspondant à la variable traitement/contrôle, ainsi que des effets aléatoires liés aux systèmes biologiques du corps humain auxquels sont attribués les effets indésirables considérés.

Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

On estimation and influence diagnostics for log-Birnbaum-Saunders Student-t regression models: Full Bayesian analysis

The purpose of this paper is to develop a Bayesian approach for log-Birnbaum-Saunders Student-t regression models under right-censored survival data. Markov chain Monte Carlo (MCMC) methods are used to develop a Bayesian procedure for the considered model. In order to attenuate the influence of the outlying observations on the parameter estimates, we present in this paper Birnbaum-Saunders models in which a Student-t distribution is assumed to explain the cumulative damage. Also, some discussions on the model selection to compare the fitted models are given and case deletion influence diagnostics are developed for the joint posterior distribution based on the Kullback-Leibler divergence. The developed procedures are illustrated with a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Power series generalized nonlinear models

We introduce in this paper a new class of discrete generalized nonlinear models to extend the binomial, Poisson and negative binomial models to cope with count data. This class of models includes some important models such as log-nonlinear models, logit, probit and negative binomial nonlinear models, generalized Poisson and generalized negative binomial regression models, among other models, which enables the fitting of a wide range of models to count data. We derive an iterative process for fitting these models by maximum likelihood and discuss inference on the parameters. The usefulness of the new class of models is illustrated with an application to a real data set. (C) 2008 Elsevier B.V. All rights reserved.

Gamma Knife(A (R)) 3-D Dose Distribution Mapping by Magnetic Resonance Imaging

In medical processes where ionizing radiation is used, dose planning and dose delivery are the key elements to patient safety and treatment success, particularly, when the delivered dose in a single session of treatment can be an order of magnitude higher than the regular doses of radiotherapy. Therefore, the radiation dose should be well defined and precisely delivered to the target while minimizing radiation exposure to surrounding normal tissues [1]. Several methods have been proposed to obtain three-dimensional (3-D) dose distribution [2, 3]. In this paper, we propose an alternative method, which can be easily implemented in any stereotactic radiosurgery center with a magnetic resonance imaging (MRI) facility. A phantom with or without scattering centers filled with Fricke gel solution is irradiated with Gamma Knife(A (R)) system at a chosen spot. The phantom can be a replica of a human organ such as head, breast or any other organ. It can even be constructed from a real 3-D MR image of an organ of a patient using a computer-aided construction and irradiated at a specific region corresponding to the tumor position determined by MRI. The spin-lattice relaxation time T (1) of different parts of the irradiated phantom is determined by localized spectroscopy. The T (1)-weighted phantom images are used to correlate the image pixels intensity to the absorbed dose and consequently a 3-D dose distribution with a high resolution is obtained.

Random number generators for the generalized Birnbaum-Saunders distribution

The generalized Birnbaum-Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum-Saunders models are compared by using this estimation method.

An extension of the generalized Birnbaum-Saunders distribution

In this paper we present an extension of the generalized Birnbaum-Saunders distribution family introduced in [Diaz-Garcia, J.A., Leiva-Sanchez, V., 2005. A new family of life distributions based on the contoured elliptically distributions. Journal of Statistical Planning and Inference 128 (2), 445-457] with a view to make it even more flexible in terms of its kurtosis coefficient. Properties involving moments and asymmetry and kurtosis indexes are studied for some special members of this family such as the slash Birnbaum-Saunders and slash-t Birnbaum-Saunders. Simulation studies for some particular cases and a real data analysis are also reported, illustrating the usefulness of the extension considered. (C) 2008 Elsevier B.V. All rights reserved.

Bayesian Analysis for the Generalized Lognormal Distribution Applied to Failure Time Analysis

There are several versions of the lognormal distribution in the statistical literature, one is based in the exponential transformation of generalized normal distribution (GN). This paper presents the Bayesian analysis for the generalized lognormal distribution (logGN) considering independent non-informative Jeffreys distributions for the parameters as well as the procedure for implementing the Gibbs sampler to obtain the posterior distributions of parameters. The results are used to analyze failure time models with right-censored and uncensored data. The proposed method is illustrated using actual failure time data of computers.

A Generalized Log-Normal Model for Grouped Survival Data

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Measurement of the shape of the boson rapidity distribution for p(p)over-bar -> Z/gamma(*)-> e(+)e(-)+X events produced at root s of 1.96 TeV

We present a measurement of the shape of the boson rapidity distribution for p (p) over bar -> Z/gamma(*)-> e(+)e(-)+X events at a center-of-mass energy of 1.96 TeV. The measurement is made for events with electron-positron mass 71 < M-ee < 111 GeV and uses 0.4 fb(-1) of data collected at the Fermilab Tevatron collider with the D0 detector. This measurement significantly reduces the uncertainties on the rapidity distribution in the forward region compared with previous measurements. Predictions of next-to-next-to-leading order (NNLO) QCD are found to agree well with the data over the full rapidity range.

Measurement of the normalized Z/gamma* -> mu(+)mu(-) transverse momentum distribution in p(p)over-bar collisions at root s=1.96 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Measurement of the shape of the boson-transverse momentum distribution in p(p)over-bar -> Z/gamma*-> e(+)e(-)+X events produced at root s=1.96 TeV

We present a measurement of the shape of the Z/gamma* boson transverse momentum (q(T)) distribution in p (p) over bar -> Z/gamma(*)-> e(+)e(-)+X events at a center-of-mass energy of 1.96 TeV using 0.98 fb(-1) of data collected with the D0 detector at the Fermilab Tevatron collider. The data are found to be consistent with the resummation prediction at low q(T), but above the perturbative QCD calculation in the region of q(T)> 30 GeV/c. Using events with q(T)< 30 GeV/c, we extract the value of g(2), one of the nonperturbative parameters for the resummation calculation. Data at large boson rapidity y are compared with the prediction of resummation and with alternative models that employ a resummed form factor with modifications in the small Bjorken x region of the proton wave function.