The MELBS team winning entry for the EVA2017 competition for spatiotemporal prediction of extreme rainfall using generalized extreme value quantiles

We present our winning entry for the EVA2017 challenge on spatiotemporal prediction of extreme precipitation. The aim of the competition is to predict extreme rainfall quantiles that score as low as possible on the competition error metric. Good or bad predictions are defined only by the metric used. Our methodology was simple and produced accurate predictions under this metric. This outcome emphasizes the importance of cross-validation and identifying model over-fitting.     

Detecting a conditional extreme value model

In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value model assumes a domain of attraction condition on a sub-collection of the components of a multivariate random vector. This model has been studied in Heffernan and Tawn (JRSS B 66(3):497–546, 2004), Heffernan and Resnick (Ann Appl Probab 17(2):537–571, 2007), and Das and Resnick (2009). In this paper we propose three statistics which act as tools to detect this model in a bivariate set-up. In addition, the proposed statistics also help to distinguish between two forms of the limit measure that is obtained in the model.     

Vector generalized linear and additive extreme value models

Over recent years parametric and nonparametric regression has slowly been adopted into extreme value data analysis. Its introduction has been characterized by piecemeal additions and embellishments, which has had a negative effect on software development and usage. The purpose of this article is to convey the classes of vector generalized linear and additive models (VGLMs and VGAMs) as offering significant advantages for extreme value data analysis, providing flexible smoothing within a unifying framework. In particular, VGLMs and VGAMs allow all parameters of extreme value distributions to be modelled as linear or smooth functions of covariates. We implement new auxiliary methodology by incorporating a quasi-Newton update for the working weight matrices within an iteratively reweighted least squares (IRLS) algorithm. A software implementation by the first author, called the vgam package for , is used to illustrate the potential of VGLMs and VGAMs.     

A model for structural safety using the extreme value approach

A new method of evaluating the safety of a structure using the maximum mean largest value concept is introduced. The paper is characterized by the following points: The maximum probability of failure is defined by employing the upper bound of load and the lower bound of resistance, that is, the structural safety is evaluated under the worst-state both for load and resistance. This is a distribution-free approach to the concept of structural safety, and the probability of failure is calculated without assuming the probability density distributions of load and resistance. Three new characteristics are introduced so that the character of the data is strongly reflected on the estimation of the maximum probability of failure. A numerical example is given using the test data.     

A choice probability characterization of generalized extreme value models

A set of necessary and sufficient conditions is established for the representability of choice probabilities by additive random utility models with generalized extreme value (GEV) distributions of utilities. These conditions yield an operational testing procedure for GEV-representability which does not require explicit construction of the underlying distribution of utilities. In addition, this characterization of GEV models reveals a number of their underlying behavioral features.     

Transition kernels and the conditional extreme value model

Classical multivariate extreme value modelling assumes that the joint distribution belongs to a multivariate domain of attraction and this assumption requires that each marginal distribution be individually attracted to a univariate extreme value distribution. The Heffernan and Tawn (J R Stat Soc Ser B (Stat Methodol) 66(3):497–546, 2004) alternative extremal model for multivariate data does not require all the components belong to an extremal domain of attraction but assumes instead the existence of an asymptotic approximation to the conditional distribution of the random vector given one of the components is extreme. Combined with the knowledge that the conditioning component belongs to a univariate domain of attraction, this leads to an approximation of the probability of certain risk regions. The original focus on conditional distributions has technical drawbacks but is a natural assumption in many contexts. The technical drawbacks are overcome by relying on convergence of measures and the theory of extended regular variation Heffernan and Resnick (Ann Appl Probab 17(2):537–71, 2007); Das and Resnick (Extremes 14(1):29–61, 2000a); Das et al. (Adv Appl Probab 45(1):139–163, 2013). We compare the two approaches and describe in what way relying on variational limit properties of conditional distributions restricts the class of limit approximations.     

Some inferences of the generalized extreme value distribution based on record values

Several distributional properties of the record values from the generalized extreme value distribution are discussed. Some recurrence relations of the moments are given. The problem of the estimation of the location and scale parameter is studied. Several estimators of the shape parameter are also discussed. Predictors of the sth record value based on the first m (m<s) record values are derived. Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part II, Eger, Hungary, 1994.     

适合中小型制造企业的客户信用评估的研究

本在对中小型制造企业的客户管理调研基础上，建立了适合中小型制造企业的信用评估指标体系，提出了基于AHP、TOPSIS和聚类分析的客户信用评估方法，并在上海某企业进行了实践，取得了较好的效果。     

Estimation of the extreme value and the extreme points

Summary Letf be a continuous function defined on some domainA andX ₁,X ₂, ... be iid random variables. We estimate the extreme value off onA by studying the limiting distribution of min {f(X ₁), ...,f(X _n )} or max {f(X ₁), ...,f(X _n )} properly normalized. Sufficient conditions for the existence of the limiting distribution as well as a characterization of the limiting distribution relative to the extreme points off will be provided. A discussion of the multidimensional case is also carried out. Partially supported by CNPq-No. 301508/84.     

The general linear model and the generalized singular value decomposition

A new derivation is given for the generalized singular value decomposition of two matrices X and F having the same number of rows. It is shown how this decomposition reveals the structure of the general Gauss-Markov linear model (y, Xβ, σ²FF′), and exhibits the structure and solution of the generalized linear least squares problem used to provide the best linear unbiased estimator for the model. The decomposition is used to prove optimality of the estimator and to reveal the structure of the covariance matrix of the error of the estimator.     

On a generalized X-ray transform and a new method for defect detection using the medium electronic density

We consider a generalization of the X-ray transform which maps a function $\text{f(}\text{V}\text{)}$ defined in $\text{R}{}^3$ onto its integrals over a pair of parallel straight lines and not over a single straight line as in a conventional X-ray transform. This new transformation arises from the image formation by double Compton-scattered radiation in transmission imaging. The problem of reconstructing $\text{f(}\text{V}\text{)}$ from its line pair integrals is formulated as an inverse problem for this generalized X-ray transform. Exploiting the line duality in the new transformation, we derive an equivalent nonlinear integral equation for $\text{f(}\text{V}\text{)}$. Special classes of solutions can be constructed. They may serve as basis for a new method of defect detection, using the medium electronic density, in non-destructive inspection. To cite this article: M.K. Nguyen, T.T. Truong, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

The extreme value of the generalized distances of the individual points in the multivariate normal sample

1. Summary The extreme value of the generalized distances, from the origin, ofN individual points which may be correlated each other, in thep-variate normal sample is defined and discussed. It contains, as special cases, (i) the extreme deviate from the population mean or the sample mean, (ii) the extreme deviate from the control variate and (iii) the range defined by (2.10) or (2.11) below. The exact sampling distributional theory of this statistic is extremely difficult to find, even its moments. However, the method of obtaining the approximate upper 100α percentage points for the ordinary significance levelα is given. The lower percentage points can be obtained in the similar way if necessary. In connection with the evaluation of the approximate percentage points, the two-dimensional chi-square distribution is discussed and the asymptotic formulas for the joint distribution function of the two generalized distances are given in the special forms for the present aim. The extreme deviate from the sample mean will be explained in some detail and the tables of the approximate upper 5, 2.5 and 1% points are given. For the cases (ii) and (iii) mentioned above the details are omitted and will be discussed in the case of need.     

Multiscale model reduction for a thermoelastic model with phase change using a generalized multiscale finite-element method

Theoretical and Mathematical Physics - The development of the cryolithozone requires building and numerically implementing mathematical models of multiphysics thermoelastic processes involving with...     

Queueing network modelling of flexible manufacturing system using mean value analysis

In the present investigation, we develop queueing model for the performance prediction of flexible manufacturing systems (FMSs) with a multiple discrete material-handling devices (MHD). An iterative method has been suggested using mean value analysis (MVA) for the state-dependent routing. Two queueing network models are considered to determine the material-handling device interference. In the first one, we model the interference from the MHD by inflating the station service times but neglect queueing at the MHD. In another network, the queueing for the MHD is taken into consideration. The performance of FMS configuration is obtained by iterating between two networks. The suggested algorithms demonstrate better results than the algorithm used by earlier workers for single MHD. Some performance indices viz. throughput, mean service time, mean waiting time, etc. are obtained. Numerical results are provided to highlight the effect of the system parameters on performance indices, which are further evaluated by using neuro-fuzzy controller system to validate the tactability of soft computing approach.     

Economic and financial prediction using rough sets model

A state-of-the-art review of the literature related to economic and financial prediction using rough sets model is presented, with special emphasis on the business failure prediction, database marketing and financial investment. These three applications require the accurate prediction of the future states based on the identification of patterns in the historical data. In addition, the historical data are in the format of a multi-attribute information table. All these conditions suit the rough sets model, an effective tool for multi-attribute classification problems. The different rough sets models and issues concerning the implementation of rough sets model – indicator selection, discretization and validation test, are also discussed in this paper. This paper will demonstrate that rough sets model is applicable to a wide range of practical problems pertaining to economic and financial prediction. In addition, the results show that the rough sets model is a promising alternative to the conventional methods for economic and financial prediction.