Adaptively weighted maximum likelihood estimation of discrete distributions

SummaryDiscrete data arise in various research fields, typically when the observations are count data.I propose a robust and efficient parametric procedure for estimation of discrete distributions. The estimation is done in two phases. First, a very robust, but possibly inefficient, estimate of the model parameters is computed and used to indentify outliers. Then the outliers are either removed from the sample or given low weights, and a weighted maximum likelihood estimate (WML) is computed.The weights are determined via an adaptive process such that if the data follow the model, then asymptotically no observation is downweighted.I prove that the final estimator inherits the breakdown point of the initial one, and that its influence function at the model is the same as the influence function of the maximum likelihood estimator, which strongly suggests that it is asymptotically fully efficient.The initial estimator is a minimum disparity estimator (MDE). MDEs can be shown to have full asymptotic efficiency, and some MDEs have very high breakdown points and very low bias under contamination. Several initial estimators are considered, and the performances of the WMLs based on each of them are studied.It results that in a great variety of situations the WML substantially improves the initial estimator, both in terms of finite sample mean square error and in terms of bias under contamination. Besides, the performances of the WML are rather stable under a change of the MDE even if the MDEs have very different behaviors.Two examples of application of the WML to real data are considered. In both of them, the necessity for a robust estimator is clear: the maximum likelihood estimator is badly corrupted by the presence of a few outliers.This procedure is particularly natural in the discrete distribution setting, but could be extended to the continuous case, for which a possible procedure is sketched.RésuméLes données discrètes sont présentes dans différents domaines de recherche, en particulier lorsque les observations sont des comptages.Je propose une méthode paramétrique robuste et efficace pour l'estimation de distributions discrètes. L'estimation est faite en deux phases. Tout d'abord, un estimateur très robuste des paramètres du modèle est calculé, et utilisé pour la détection des données aberrantes (outliers). Cet estimateur n'est pas nécessairement efficace. Ensuite, soit les outliers sont retirés de l'échantillon, soit des faibles poids leur sont attribués, et un estimateur du maximum de vraisemblance pondéré (WML) est calculé.Les poids sont déterminés via un processus adaptif, tel qu'asymptotiquement, si les données suivent le modèle, aucune observation n'est dépondérée.Je prouve que le point de rupture de l'estimateur final est au moins aussi élevé que celui de l'estimateur initial, et que sa fonction d'influence au modèle est la même que celle du maximum de vraisemblance, ce qui suggère que cet estimateur est pleinement efficace asymptotiquement.L'estimateur initial est un estimateur de disparité minimale (MDE). Les MDE sont asymptotiquement pleinement efficaces, et certains d'entre eux ont un point de rupture très élevé et un très faible biais sous contamination. J'étudie les performances du WML basé sur différents MDEs.Le résultat est que dans une grande variété de situations le WML améliore largement les performances de l'estimateur initial, autant en terme du carré moyen de l'erreur que du biais sous contamination. De plus, les performances du WML restent assez stables lorsqu'on change l'estimateur initial, même si les différents MDEs ont des comportements très différents.Je considère deux exemples d'application du WML à des données réelles, où la nécessité d'un estimateur robuste est manifeste : l'estimateur du maximum de vraisemblance est fortement corrompu par la présence de quelques outliers.La méthode proposée est particulièrement naturelle dans le cadre des distributions discrètes, mais pourrait être étendue au cas continu.

A methodology for the adaptation of a PMP at the determination of a PMF

This paper presents a new type of very fine grid hydrological model based on the spatiotemporal repartition of a PMP (Probable Maximum Precipitation) and on the topography. The goal is to estimate the influence of this rain on a PMF (Probable Maximum Flood) on a catchment area in Switzerland. The spatiotemporal distribution of the PMP was realized using six clouds modeled by the advection-diffusion equation. The equation shows the movement of the clouds over the terrain and also gives the evolution of the rain intensity in time. This hydrological modeling is followed by a hydraulic modeling of the surface and subterranean flow, done considering the factors that contribute to the hydrological cycle, such as the infiltration, the resurgence and the snowmelt. These added factors make the developed model closer to reality and also offer flexibility in the initial condition that is added to the factors concerning the PMP, such as the duration of the rain, the speed and direction of the wind. All these initial conditions taken together offer a complete image of the PMF.

Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?

An overview is given on a study which showed that not only in chemical reactions but also in the favorable case of nontotally symmetric vibrations where the chemical and external potentials keep approximately constant, the generalized maximum hardness principle (GMHP) and generalized minimum polarizability principle (GMPP) may not be obeyed. A method that allows an accurate determination of the nontotally symmetric molecular distortions with more marked GMPP or anti-GMPP character through diagonalization of the polarizability Hessian matrix is introduced

Inundações urbanas: desafios ao ordenamento do território. O caso da Cidade da Praia (Cabo Verde)

Pela sua posição geográfica e particulares condições climáticas, devidas à sua inserção na faixa saheliana com caraterísticas de marcada aridez, Cabo Verde é um arquipélago com condições naturais adversas, pautado principalmente pela seca prolongada. Muitas vezes esta conjuntura é interpolada por curtos períodos de fortes chuvadas que podem originar cheias e inundações nos principais centros urbanos. Os eventos ocorridos revelam consequências graves, desde prejuízos na agricultura, perda de animais, destruição de infra-estruturas, perda de bens materiais e, mesmo, vítimas humanas mortais. Este estudo tem como objetivos principais: (i) perceber os problemas e desafios que se colocam à cidade da Praia (maior centro urbano do país, com forte crescimento e expansão urbana) perante situações de inundação; (ii) contribuir para o maior conhecimento das causas e consequências dessas inundações; (iii) definir quais as áreas de maior suscetibilidade às cheias e quais as que possuem um maior risco potencial. Optou-se por uma metodologia integrada, através do levantamento bibliográfico, cartográfico, numérico e percetivo (com base em entrevistas e inquéritos). Para o estudo das bacias hidrográficas foram calculados índices morfométricos, definidas classes de permeabilidade do substrato geológico e aplicado o método multicritério de Reis (2011) para a definição das áreas suscetíveis às cheias. Analisaram-se as precipitações máximas diárias anuais e respetivos períodos de retorno, com a aplicação do método de Gumbel. A análise de notícias de jornais, referentes ao período compreendido entre 1980 e 2011, foi fundamental para o conhecimento da distribuição espácio-temporal dos eventos perigosos de inundação em Cabo Verde e na cidade da Praia. Os resultados obtidos revelam um significativo grau de suscetibilidade às cheias na cidade da Praia. As áreas de maior risco potencial às inundações encontram-se no setor central da cidade, resultante da conjugação da convergência do escoamento das três ribeiras principais, da elevada densidade populacional e de construção desordenada nos leitos de cheia e nas áreas deprimidas, onde se acumulam as águas.

A new chance-constrained maximum capture location problem

The paper presents a new model based on the basic Maximum Capture model,MAXCAP. The New Chance Constrained Maximum Capture modelintroduces astochastic threshold constraint, which recognises the fact that a facilitycan be open only if a minimum level of demand is captured. A metaheuristicbased on MAX MIN ANT system and TABU search procedure is presented tosolve the model. This is the first time that the MAX MIN ANT system isadapted to solve a location problem. Computational experience and anapplication to 55 node network are also presented.

Inundações Urbanas - Desafios ao Ordenamento do Território - O

Pela sua posição geográfica e particulares condições climáticas, devidas à sua inserção na faixa saheliana com caraterísticas de marcada aridez, Cabo Verde é um arquipélago com condições naturais adversas, pautado principalmente pela seca prolongada. Muitas vezes esta conjuntura é interpolada por curtos períodos de fortes chuvadas que podem originar cheias e inundações nos principais centros urbanos. Os eventos ocorridos revelam consequências graves, desde prejuízos na agricultura, perda de animais, destruição de infra-estruturas, perda de bens materiais e, mesmo, vítimas humanas mortais. Este estudo tem como objetivos principais: (i) perceber os problemas e desafios que se colocam à cidade da Praia (maior centro urbano do país, com forte crescimento e expansão urbana) perante situações de inundação; (ii) contribuir para o maior conhecimento das causas e consequências dessas inundações; (iii) definir quais as áreas de maior suscetibilidade às cheias e quais as que possuem um maior risco potencial. Optou-se por uma metodologia integrada, através do levantamento bibliográfico, cartográfico, numérico e percetivo (com base em entrevistas e inquéritos). Para o estudo das bacias hidrográficas foram calculados índices morfométricos, definidas classes de permeabilidade do substrato geológico e aplicado o método multicritério de Reis (2011) para a definição das áreas suscetíveis às cheias. Analisaram-se as precipitações máximas diárias anuais e respetivos períodos de retorno, com a aplicação do método de Gumbel. A análise de notícias de jornais, referentes ao período compreendido entre 1980 e 2011, foi fundamental para o conhecimento da distribuição espácio-temporal dos eventos perigosos de inundação em Cabo Verde e na cidade da Praia. Os resultados obtidos revelam um significativo grau de suscetibilidade às cheias na cidade da Praia. As áreas de maior risco potencial às inundações encontram-se no setor central da cidade, resultante da conjugação da convergência do escoamento das três ribeiras principais, da elevada densidade populacional e de construção desordenada nos leitos de cheia e nas áreas deprimidas, onde se acumulam as águas.

Seasonality of insects in the semi-arid Caatinga of northeastern Brazil

Insects are essential to tropical ecosystems functioning. In semi-arid regions, the increase in abundance and/or activity (e.g. reproduction and foraging behavior) of insects is usually associated with climatic variables. The present study investigates which climatic variables are best predictors of insect abundance in an area of Caatinga in northeastern Brazil. Individuals were sampled for 24 months using Malaise and pitfall traps, and beating trays. A total of 58925 individuals belonging to 20 insect orders were collected. The most abundant orders were Hymenoptera, Diptera, Collembola and Coleoptera. Most orders studied showed a clear maximum abundance in the rainy season. Rainfall and humidity were the best predictors of insect abundance in the Caatinga. However, no climatic variable could explain Psocoptera and Blattodea variance in abundance/activity. Our results suggest that climatic changes associated with rainfall patterns in the Caatinga may affect ecosystem processes and services that depend direct or indirectly on insect abundance/activity.

An experimental test of rainfall as a control agent of Glycaspis brimblecombei Moore (Hemiptera, Psyllidae) on seedlings of Eucalyptus camaldulensis Dehn (Myrtaceae)

An experimental test of rainfall as a control agent of Glycaspis brimblecombei Moore (Hemiptera, Psyllidae) on seedlings of Eucalyptus camaldulensis Dehn (Myrtaceae). Glycaspis brimblecombei is one the greatest threats to eucalyptus plantations in Brazil. The effects of rainfall to reduce the abundance of lerp of Glycaspis brimblecombei on experimentally infested seedlings of Eucalyptus camaldulensis were assessed. The number of lerps on the adaxial and abaxial surfaces of every leaf of 60 seedlings was recorded, before and after submission to the following treatments: "artificial rain", "leaf wetting" and control. A drastic reduction in lerp abundance per plant was observed after the treatments "leaf wetting" and artificial rain (F = 53.630; p < 0.001), whereas lerp abundance remained roughly constant in the control treatment along the experiment (F = 1.450; p = 0.232). At the end of the experiment, lerp abundance was significantly lower in both the "artificial rain" and "leaf wetting" than in the control treatment. Two days of rainfall simulation were sufficient to decrease more than 50% of the lerp population, with almost 100% of effectiveness after 5 days of experiment. Our results indicate that lerp solubilization and mechanical removal by water are potential tools to the population regulation of G. brimblecombei on E. camaldulensis seedlings.

Maximum-likelihood estimation of specific differential phase and attenuation in rain

Precise estimation of propagation parameters inprecipitation media is of interest to improve the performanceof communications systems and in remote sensing applications.In this paper, we present maximum-likelihood estimators ofspecific attenuation and specific differential phase in rain. Themodel used for obtaining the cited estimators assumes coherentpropagation, reflection symmetry of the medium, and Gaussianstatistics of the scattering matrix measurements. No assumptionsabout the microphysical properties of the medium are needed.The performance of the estimators is evaluated through simulateddata. Results show negligible estimators bias and variances closeto Cramer–Rao bounds.

Avaliação de Panicum maximum jacq. para tolerância ao alumínio em solução nutritiva

Em condições controladas de temperatura, umidade e iluminação, 30 genótipos de Panicum maximum foram avaliados para a verificação de tolerância às doses de alumínio de 0, 12 e 24 mg L-1 em solução nutritiva. Os efeitos do alumínio na inibição do alongamento radicular e no índice de tolerância possibilitaram a estratificação dos genótipos em três categorias: tolerantes, intermediários e sensíveis. A maior parte dos genótipos apresentou de média a baixa tolerância ao alumínio, destacando-se, como os mais tolerantes, os genótipos K191, T95, T84, T91 e Centenário e, como os mais sensíveis, os genótipos Centauro, K68, K214 e T46.

Anomalous rainfall and associated atmospheric circulation in the northeast Spanish Mediterranean area and its relationship to sediment fluidization events in a lake

Changes in the dynamics of sediment transport in a Mediterranean lake (sediment fluidization events) are linked to atmospheric circulations patterns (trough monthly precipitation). In the basins of Lake Banyoles, located in the northeast of Spain, water enters mainly through subterranean springs, and associated fluctuations in the vertical migration of sediment distribution (fluidization events) present episodic behavior as a result of episodic rainfall in the area. The initiation of the fluidization events takes place when the monthly rainfall is ∼2.7 times greater than the mean monthly rainfall of the rainiest months in the area, especially in spring (April and May), October, and December. The duration of these events is found to be well correlated with the accumulated rainfall of the preceding 10 months before the process initiation. The rainfall, in turn, is mainly associated with six atmospheric circulation patterns among the 19 fundamental circulations that emerged in an earlier study focused on significant rainfall days in Mediterranean Spain. Among them, accentuated surface lows over the northeast of Spain, general northeasterly winds by low pressure centered to the east of Balearic Islands and short baroclinic waves over the Iberian Peninsula, with easterly flows over the northeastern coast of Spain, are found the most relevant atmospheric circulations that drive heavy rainfall events

The second law of thermodynamics and the global climate system : A review of the maximum entropy production principle

The long-term mean properties of the global climate system and those of turbulent fluid systems are reviewed from a thermodynamic viewpoint. Two general expressions are derived for a rate of entropy production due to thermal and viscous dissipation (turbulent dissipation) in a fluid system. It is shown with these expressions that maximum entropy production in the Earth s climate system suggested by Paltridge, as well as maximum transport properties of heat or momentum in a turbulent system suggested by Malkus and Busse, correspond to a state in which the rate of entropy production due to the turbulent dissipation is at a maximum. Entropy production due to absorption of solar radiation in the climate system is found to be irrelevant to the maximized properties associated with turbulence. The hypothesis of maximum entropy production also seems to be applicable to the planetary atmospheres of Mars and Titan and perhaps to mantle convection. Lorenz s conjecture on maximum generation of available potential energy is shown to be akin to this hypothesis with a few minor approximations. A possible mechanism by which turbulent fluid systems adjust themselves to the states of maximum entropy production is presented as a selffeedback mechanism for the generation of available potential energy. These results tend to support the hypothesis of maximum entropy production that underlies a wide variety of nonlinear fluid systems, including our planet as well as other planets and stars

States of maximum entropy production in a onedimensional vertical model with convective adjustment

We investigate the hypothesis that the atmosphere is constrained to maximize its entropy production by using a one-dimensional (1-D) vertical model. We prescribe the lapse rate in the convective layer as that of the standard troposphere. The assumption that convection sustains a critical lapse rate was absent in previous studies, which focused on the vertical distribution of climatic variables, since such a convective adjustment reduces the degrees of freedom of the system and may prevent the application of the maximum entropy production (MEP) principle. This is not the case in the radiative–convective model (RCM) developed here, since we accept a discontinuity of temperatures at the surface similar to that adopted in many RCMs. For current conditions, the MEP state gives a difference between the ground temperature and the air temperature at the surface ≈10 K. In comparison, conventional RCMs obtain a discontinuity ≈2 K only. However, the surface boundary layer velocity in the MEP state appears reasonable (≈3 m s-¹). Moreover, although the convective flux at the surface in MEP states is almost uniform in optically thick atmospheres, it reaches a maximum value for an optical thickness similar to current conditions. This additional result may support the maximum convection hypothesis suggested by Paltridge (1978)