Transformation kernel density estimation of actuarial loss functions

[cat] Es presenta un estimador nucli transformat que és adequat per a distribucions de cua pesada. Utilitzant una transformació basada en la distribució de probabilitat Beta l’elecció del paràmetre de finestra és molt directa. Es presenta una aplicació a dades d’assegurances i es mostra com calcular el Valor en Risc.

The Lorenz-maximal core allocations and the kernel in some classes of assignment games

En aquest treball demostrem que en la classe de jocs d'assignació amb diagonal dominant (Solymosi i Raghavan, 2001), el repartiment de Thompson (que coincideix amb el valor tau) és l'únic punt del core que és maximal respecte de la relació de dominància de Lorenz, i a més coincideix amb la solucié de Dutta i Ray (1989), també coneguda com solució igualitària. En segon lloc, mitjançant una condició més forta que la de diagonal dominant, introduïm una nova classe de jocs d'assignació on cada agent obté amb la seva parella òptima almenys el doble que amb qualsevol altra parella. Per aquests jocs d'assignació amb diagonal 2-dominant, el repartiment de Thompson és l'únic punt del kernel, i per tant el nucleolo.

Transformation kernel density estimation of actuarial loss functions

[cat] Es presenta un estimador nucli transformat que és adequat per a distribucions de cua pesada. Utilitzant una transformació basada en la distribució de probabilitat Beta l’elecció del paràmetre de finestra és molt directa. Es presenta una aplicació a dades d’assegurances i es mostra com calcular el Valor en Risc.

Local and global error models to improve uncertainty quantification

In groundwater applications, Monte Carlo methods are employed to model the uncertainty on geological parameters. However, their brute-force application becomes computationally prohibitive for highly detailed geological descriptions, complex physical processes, and a large number of realizations. The Distance Kernel Method (DKM) overcomes this issue by clustering the realizations in a multidimensional space based on the flow responses obtained by means of an approximate (computationally cheaper) model; then, the uncertainty is estimated from the exact responses that are computed only for one representative realization per cluster (the medoid). Usually, DKM is employed to decrease the size of the sample of realizations that are considered to estimate the uncertainty. We propose to use the information from the approximate responses for uncertainty quantification. The subset of exact solutions provided by DKM is then employed to construct an error model and correct the potential bias of the approximate model. Two error models are devised that both employ the difference between approximate and exact medoid solutions, but differ in the way medoid errors are interpolated to correct the whole set of realizations. The Local Error Model rests upon the clustering defined by DKM and can be seen as a natural way to account for intra-cluster variability; the Global Error Model employs a linear interpolation of all medoid errors regardless of the cluster to which the single realization belongs. These error models are evaluated for an idealized pollution problem in which the uncertainty of the breakthrough curve needs to be estimated. For this numerical test case, we demonstrate that the error models improve the uncertainty quantification provided by the DKM algorithm and are effective in correcting the bias of the estimate computed solely from the MsFV results. The framework presented here is not specific to the methods considered and can be applied to other combinations of approximate models and techniques to select a subset of realizations

Pedotransfer functions to estimate proctor test parameters under different tillage systems

The Proctor test is time-consuming and requires sampling of several kilograms of soil. Proctor test parameters were predicted in Mollisols, Entisols and Vertisols of the Pampean region of Argentina under different management systems. They were estimated from a minimum number of readily available soil properties (soil texture, total organic C) and management (training data set; n = 73). The results were used to generate a soil compaction susceptibility model, which was subsequently validated using a second group of independent data (test data set; n = 24). Soil maximum bulk density was estimated as follows: Maximum bulk density (Mg m-3) = 1.4756 - 0.00599 total organic C (g kg-1) + 0.0000275 sand (g kg-1) + 0.0539 management. Management was equal to 0 for uncropped and untilled soils and 1 for conventionally tilled soils. The established models predicted the Proctor test parameters reasonably well, based on readily available soil properties. Tillage systems induced changes in the maximum bulk density regardless of total organic matter content or soil texture. The lower maximum apparent bulk density values under no-tillage require a revision of the relative compaction thresholds for different no-tillage crops.

Method to estimate soil macroporosity and microporosity based on sand content and bulk density

Macroporosity is often used in the determination of soil compaction. Reduced macroporosity can lead to poor drainage, low root aeration and soil degradation. The aim of this study was to develop and test different models to estimate macro and microporosity efficiently, using multiple regression. Ten soils were selected within a large range of textures: sand (Sa) 0.07-0.84; silt 0.03-0.24; clay 0.13-0.78 kg kg-1 and subjected to three compaction levels (three bulk densities, BD). Two models with similar accuracy were selected, with a mean error of about 0.02 m³ m-3 (2 %). The model y = a + b.BD + c.Sa, named model 2, was selected for its simplicity to estimate Macro (Ma), Micro (Mi) or total porosity (TP): Ma = 0.693 - 0.465 BD + 0.212 Sa; Mi = 0.337 + 0.120 BD - 0.294 Sa; TP = 1.030 - 0.345 BD 0.082 Sa; porosity values were expressed in m³ m-3; BD in kg dm-3; and Sa in kg kg-1. The model was tested with 76 datum set of several other authors. An error of about 0.04 m³ m-3 (4 %) was observed. Simulations of variations in BD as a function of Sa are presented for Ma = 0 and Ma = 0.10 (10 %). The macroporosity equation was remodeled to obtain other compaction indexes: a) to simulate maximum bulk density (MBD) as a function of Sa (Equation 11), in agreement with literature data; b) to simulate relative bulk density (RBD) as a function of BD and Sa (Equation 13); c) another model to simulate RBD as a function of Ma and Sa (Equation 16), confirming the independence of this variable in relation to Sa for a fixed value of macroporosity and, also, proving the hypothesis of Hakansson & Lipiec that RBD = 0.87 corresponds approximately to 10 % macroporosity (Ma = 0.10 m³ m-3).

Evaluation of Sikora instead of SMP buffer to estimate the potential acidity of brazilian soils

Despite the efficiency of the Shoemaker, McLean, Pratt (SMP) buffer method in estimating soil acidity, the presence of p-nitrophenol and potassium chromate in the solution, both hazardous substances, has caused increasing environmental concerns. The purpose of this study was to test Sikora method (Sikora, 2006) as an alternative to the adapted SMP buffer method, generally used to estimate potential acidity of Southern Brazilian soils. For the test, 21 soils in the South and Cerrado regions of Brazil were sampled. (1) The potential acidity values of these soils range from 35.95 to 4.02 cmol c kg-1 of soil, reflecting a wide acidity variation. The Sikora buffer does not mimic the adapted SMP buffer used in Southern Brazil, since the former has a low ability to distinguish soils with different acidity from each other, probably due to the higher buffer capacity than of the adapted SMP solution.

Replication of an ivg protocol to estimate bioaccessible arsenic in materials from a gold mining area in Brazil

Tests for bioaccessibility are useful in human health risk assessment. No research data with the objective of determining bioaccessible arsenic (As) in areas affected by gold mining and smelting activities have been published so far in Brazil. Samples were collected from four areas: a private natural land reserve of Cerrado; mine tailings; overburden; and refuse from gold smelting of a mining company in Paracatu, Minas Gerais. The total, bioaccessible and Mehlich-1-extractable As levels were determined. Based on the reproducibility and the accuracy/precision of the in vitro gastrointestinal (IVG) determination method of bioaccessible As in the reference material NIST 2710, it was concluded that this procedure is adequate to determine bioaccessible As in soil and tailing samples from gold mining areas in Brazil. All samples from the studied mining area contained low percentages of bioaccessible As.

Pedotransfer functions to estimate water retention parameters of soils in northeastern Brazil

Pedotransfer functions (PTF) were developed to estimate the parameters (α, n, θr and θs) of the van Genuchten model (1980) to describe soil water retention curves. The data came from various sources, mainly from studies conducted by universities in Northeast Brazil, by the Brazilian Agricultural Research Corporation (Embrapa) and by a corporation for the development of the São Francisco and Parnaíba river basins (Codevasf), totaling 786 retention curves, which were divided into two data sets: 85 % for the development of PTFs, and 15 % for testing and validation, considered independent data. Aside from the development of general PTFs for all soils together, specific PTFs were developed for the soil classes Ultisols, Oxisols, Entisols, and Alfisols by multiple regression techniques, using a stepwise procedure (forward and backward) to select the best predictors. Two types of PTFs were developed: the first included all predictors (soil density, proportions of sand, silt, clay, and organic matter), and the second only the proportions of sand, silt and clay. The evaluation of adequacy of the PTFs was based on the correlation coefficient (R) and Willmott index (d). To evaluate the PTF for the moisture content at specific pressure heads, we used the root mean square error (RMSE). The PTF-predicted retention curve is relatively poor, except for the residual water content. The inclusion of organic matter as a PTF predictor improved the prediction of parameter a of van Genuchten. The performance of soil-class-specific PTFs was not better than of the general PTF. Except for the water content of saturated soil estimated by particle size distribution, the tested models for water content prediction at specific pressure heads proved satisfactory. Predictions of water content at pressure heads more negative than -0.6 m, using a PTF considering particle size distribution, are only slightly lower than those obtained by PTFs including bulk density and organic matter content.

Pedotransfer functions to estimate retention and availability of water in soils of the state of Santa Catarina, Brazil

Studies on water retention and availability are scarce for subtropical or humid temperate climate regions of the southern hemisphere. The aims of this study were to evaluate the relations of the soil physical, chemical, and mineralogical properties with water retention and availability for the generation and validation of continuous point pedotransfer functions (PTFs) for soils of the State of Santa Catarina (SC) in the South of Brazil. Horizons of 44 profiles were sampled in areas under different cover crops and regions of SC, to determine: field capacity (FC, 10 kPa), permanent wilting point (PWP, 1,500 kPa), available water content (AW, by difference), saturated hydraulic conductivity, bulk density, aggregate stability, particle size distribution (seven classes), organic matter content, and particle density. Chemical and mineralogical properties were obtained from the literature. Spearman's rank correlation analysis and path analysis were used in the statistical analyses. The point PTFs for estimation of FC, PWP and AW were generated for the soil surface and subsurface through multiple regression analysis, followed by robust regression analysis, using two sets of predictive variables. Soils with finer texture and/or greater organic matter content retain more moisture, and organic matter is the property that mainly controls the water availability to plants in soil surface horizons. Path analysis was useful in understanding the relationships between soil properties for FC, PWP and AW. The predictive power of the generated PTFs to estimate FC and PWP was good for all horizons, while AW was best estimated by more complex models with better prediction for the surface horizons of soils in Santa Catarina.

Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework

The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.

Advanced Kernel Methods For Remote Sensing Image Classification

Résumé Suite aux recentes avancées technologiques, les archives d'images digitales ont connu une croissance qualitative et quantitative sans précédent. Malgré les énormes possibilités qu'elles offrent, ces avancées posent de nouvelles questions quant au traitement des masses de données saisies. Cette question est à la base de cette Thèse: les problèmes de traitement d'information digitale à très haute résolution spatiale et/ou spectrale y sont considérés en recourant à des approches d'apprentissage statistique, les méthodes à noyau. Cette Thèse étudie des problèmes de classification d'images, c'est à dire de catégorisation de pixels en un nombre réduit de classes refletant les propriétés spectrales et contextuelles des objets qu'elles représentent. L'accent est mis sur l'efficience des algorithmes, ainsi que sur leur simplicité, de manière à augmenter leur potentiel d'implementation pour les utilisateurs. De plus, le défi de cette Thèse est de rester proche des problèmes concrets des utilisateurs d'images satellite sans pour autant perdre de vue l'intéret des méthodes proposées pour le milieu du machine learning dont elles sont issues. En ce sens, ce travail joue la carte de la transdisciplinarité en maintenant un lien fort entre les deux sciences dans tous les développements proposés. Quatre modèles sont proposés: le premier répond au problème de la haute dimensionalité et de la redondance des données par un modèle optimisant les performances en classification en s'adaptant aux particularités de l'image. Ceci est rendu possible par un système de ranking des variables (les bandes) qui est optimisé en même temps que le modèle de base: ce faisant, seules les variables importantes pour résoudre le problème sont utilisées par le classifieur. Le manque d'information étiquétée et l'incertitude quant à sa pertinence pour le problème sont à la source des deux modèles suivants, basés respectivement sur l'apprentissage actif et les méthodes semi-supervisées: le premier permet d'améliorer la qualité d'un ensemble d'entraînement par interaction directe entre l'utilisateur et la machine, alors que le deuxième utilise les pixels non étiquetés pour améliorer la description des données disponibles et la robustesse du modèle. Enfin, le dernier modèle proposé considère la question plus théorique de la structure entre les outputs: l'intègration de cette source d'information, jusqu'à présent jamais considérée en télédétection, ouvre des nouveaux défis de recherche. Advanced kernel methods for remote sensing image classification Devis Tuia Institut de Géomatique et d'Analyse du Risque September 2009 Abstract The technical developments in recent years have brought the quantity and quality of digital information to an unprecedented level, as enormous archives of satellite images are available to the users. However, even if these advances open more and more possibilities in the use of digital imagery, they also rise several problems of storage and treatment. The latter is considered in this Thesis: the processing of very high spatial and spectral resolution images is treated with approaches based on data-driven algorithms relying on kernel methods. In particular, the problem of image classification, i.e. the categorization of the image's pixels into a reduced number of classes reflecting spectral and contextual properties, is studied through the different models presented. The accent is put on algorithmic efficiency and the simplicity of the approaches proposed, to avoid too complex models that would not be used by users. The major challenge of the Thesis is to remain close to concrete remote sensing problems, without losing the methodological interest from the machine learning viewpoint: in this sense, this work aims at building a bridge between the machine learning and remote sensing communities and all the models proposed have been developed keeping in mind the need for such a synergy. Four models are proposed: first, an adaptive model learning the relevant image features has been proposed to solve the problem of high dimensionality and collinearity of the image features. This model provides automatically an accurate classifier and a ranking of the relevance of the single features. The scarcity and unreliability of labeled. information were the common root of the second and third models proposed: when confronted to such problems, the user can either construct the labeled set iteratively by direct interaction with the machine or use the unlabeled data to increase robustness and quality of the description of data. Both solutions have been explored resulting into two methodological contributions, based respectively on active learning and semisupervised learning. Finally, the more theoretical issue of structured outputs has been considered in the last model, which, by integrating outputs similarity into a model, opens new challenges and opportunities for remote sensing image processing.

Estimate of Groundwater Recharge Based on Water Balance in The Unsaturated Soil Zone

ABSTRACT Groundwater management depends on the knowledge on recharge rates and water fluxes within aquifers. The recharge is one of the water cycle components most difficult to estimate. As a result, despite the chosen method, the estimates are subject to uncertainties that can be identified by means of comparison with other approaches. In this study, groundwater recharge estimates based on the water balance in the unsaturated zone is assessed. Firstly, the approach is evaluated by comparing the results with those of another method. Then, the estimates are used as inputs in a transient groundwater flow model in order to assess how the water table would respond to the obtained recharges rates compared to measured levels. The results suggest a good performance of the adopted approach and, despite some inherent limitations, it has advantages over other methods since the data required are easier to obtain.