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Summary: Count data are omnipresent in many applied fields, often with overdispersion. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on how the tail behaviour of the mixing distribution is related to the tail of the resulting Poisson mixture. We define five sets of mixing distributions, and we identify for each case whenever the Poisson mixture is in, close to or far from a domain of attraction of maxima. We also characterize how the Poisson mixture behaves similarly to a standard Poisson distribution when the mixing distribution has a finite support. Finally, we study, both analytically and numerically, how goodness‐of‐fit can be assessed with the inspection of tail behaviour. [ABSTRACT FROM AUTHOR]

We present the application of two statistical artificial intelligence tools for multi-scale shallow water simulations. Artificial neural networks (ANNs) and boosted trees (BTs) are used to model the relationship between low-resolution (LR) and high-resolution (HR) information derived from simulations provided in the learning phase. The two statistical models are analyzed (and compared) through hyper-parameters such as the number of epochs and the network structure for ANNs, and the learning rate, tree depth and number for BTs. This analysis is performed through 4 numerical experiments the input datasets of which (for the learning, validation and test phases) are varied through the boundary conditions of the flow numerical simulation.The performance of the ANNs is remarkably consistent, regardless of the choice made for the training/validation/testing set. The performance improves with the number of epochs and the number of neurons. For a given number of neurons, a single-layer structure performs better than multi-layer structures. BTs perform significantly better than ANNs in 2 experiments, with an error 10 to 100 times lower and a computational cost 5 to 10 times larger). However, when the validation datasets differ from the training datasets, the performance of BTs performance is strongly degraded, with a modelling error more than one order of magnitude larger than that of ANNs.Used in conjunction with upscaled flood models such as porosity models, these techniques appear as a promising operational alternative to direct flood hazard assessment from HR flow simulations. [ABSTRACT FROM AUTHOR]

Summary: The topographical complexity of coral reefs is of primary importance for a number of hydrodynamical and ecological processes. The present study is based on a series of high‐resolution seabottom elevation measurements along the Maupiti Barrier Reef, French Polynesia. Several statistical metrics and spectral analysis are used to characterize the spatial evolution of the coral geometrical structure from the reef crest to the backreef. A consistent fractal‐like power law exists in the spectral density of bottom elevation for length scales between 0.1 and 7 m, while at larger scale, the reef structure shows a different pattern. Such a fine characterization of the reef geometrical structure provides key elements to reconstruct the reef history, to improve the representation of reef roughness in hydrodynamical models and to monitor the evolution of coral reef systems in the context of global change. © 2020 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Dose selection is one of the most difficult and crucial decisions to make during drug development. As a consequence, the dose-finding trial is a major milestone in the drug development plan and should be properly designed. This article will review the most recent methodologies for optimizing the design of dose-finding studies: all of them are based on the modeling of the dose–response curve, which is now the gold standard approach for analyzing dose-finding studies instead of the traditional ANOVA/multiple testing approach. We will address the optimization of both fixed and adaptive designs and briefly outline new methodologies currently under investigation, based on utility functions. [ABSTRACT FROM AUTHOR]

The statistical modeling of space-time extremes in environmental applications is key to understanding complex dependence structures in original event data and to generating realistic scenarios for impact models. In this context of high-dimensional data, we propose a novel hierarchical model for high threshold exceedances defined over continuous space and time by embedding a space-time Gamma process convolution for the rate of an exponential variable, leading to asymptotic independence in space and time. Its physically motivated anisotropic dependence structure is based on geometric objects moving through space-time according to a velocity vector. We demonstrate that inference based on weighted pairwise likelihood is fast and accurate. The usefulness of our model is illustrated by an application to hourly precipitation data from a study region in Southern France, where it clearly improves on an alternative censored Gaussian space-time random field model. While classical limit models based on threshold-stability fail to appropriately capture relatively fast joint tail decay rates between asymptotic dependence and classical independence, strong empirical evidence from our application and other recent case studies motivates the use of more realistic asymptotic independence models such as ours. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

In atmospheric chemistry, daily maxima concentrations capture information about the variability among peak values. Statistically, they can often be modeled by a Gumbel distribution. This is the case for two very important greenhouse gases methane and nitrous oxide maxima when they are measured at our site of interest, Gif-sur-Yvette, a city south west of Paris. In practice, those two daily concentrations are not always recorded during the same period, and it would be of interest to reconstruct one from the other one. Such a type of inference can be handled within a state space modeling framework, but state space models are not tailored to represent the dynamics among Gumbel-distributed maxima. By building on our previous work, which made a link between linear autoregressive time series and Gumbel-distributed maxima, we propose and study such a state space model. It has the advantages of being linear and of preserving the Gumbel characteristic in both the state and observational equations. Concerning the inference of the hidden maxima at the state equation level, we derive the optimal weights of the auxiliary particle filtering approach of Pitt and Shephard. A simulation study indicates that our approach offers a gain over the Kalman filter, the bootstrap filter, and the nonmodified version of the Pitt and Shephard auxiliary filter. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Recently, the topic of extreme value under random censoring has been considered. Different estimators for the index have been proposed (see Beirlant et al., 2007). All of them are constructed as the classical estimators (without censoring) divided by the proportion of non censored observations above a certain threshold. Their asymptotic normality was established by Einmahl et al. (2008). An alternative approach consists of using the Peaks-Over-Threshold method (Balkema and de Haan, 1974; Smith, 1987) and to adapt the likelihood to the context of censoring. This leads to ML-estimators whose asymptotic properties are still unknown. The aim of this article is to propose one-step approximations, based on the Newton-Raphson algorithm. Based on a small simulation study, the one-step estimators are shown to be close approximations to the ML-estimators. Also, the asymptotic normality of the one-step estimators has been established, whereas in case of the ML-estimators it is still an open problem. The proof of our result, whose approach is new in the Peaks-Over-Threshold context, is in the spirit of Lehmann's theory (1991). [ABSTRACT FROM AUTHOR]

The article presents a study on autoregressive (AR) models for maxima and their applications to methane (CH4) and nitrous oxide ( N2O). The authors impose that AR models have to follow a Gumbel distribution whose main theoretical properties are derived. The study also offers a simple way to model short-term dependencies among maxima stemming.

Max-stable processes play a fundamental role in modeling the spatial dependence of extremes because they appear as a natural extension of multivariate extreme value distributions. In practice, a well-known restrictive assumption when using max-stable processes comes from the fact that the observed extremal dependence is assumed to be related to a particular max-stable dependence structure. As a consequence, the latter is imposed to all events which are more extreme than those that have been observed. Such an assumption is inappropriate in the case of asymptotic independence. Following recent advances in the literature, we exploit a max-mixture model to suggest a general spatial model which ensures extremal dependence at small distances, possible independence at large distances and asymptotic independence at intermediate distances. Parametric inference is carried out using a pairwise composite likelihood approach. Finally we apply our modeling framework to analyze daily precipitations over the East of Australia, using block maxima over the observation period and exceedances over a large threshold. [ABSTRACT FROM AUTHOR]

Abstract: The Pareto distribution is found in a large number of real world situations and is also a well-known model for extreme events. In the spirit of Neyman [1937. Smooth tests for goodness of fit. Skand. Aktuarietidskr. 20, 149–199] and Thomas and Pierce [1979. Neyman''s smooth goodness-of-fit test when the hypothesis is composite. J. Amer. Statist. Assoc. 74, 441–445], we propose a smooth goodness of fit test for the Pareto distribution family which is motivated by LeCam''s theory of local asymptotic normality (LAN). We establish the behavior of the associated test statistic firstly under the null hypothesis that the sample follows a Pareto distribution and secondly under local alternatives using the LAN framework. Finally, simulations are provided in order to study the finite sample behavior of the test statistic. [Copyright &y& Elsevier]