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Title: Some possibilities of heteroskedasticity modeling with applications to non-life insurance Author:Petra Pavlačková Department: Department of Probability and Mathematical Statistics Supervisor: Ing. Zimmermann Pavel, Ph.d. Abstract: This thesis deals with the possibilities of modeling heteroskedasticity using generalized linear models. It summarizes the assumption for these models and their application in practice. It shows the practical need for these models. Furthermore, the thesis deals with the modeling of variance using other methods than generalized lienar models - such as generalized additive models or local regression. Comparison of methods is graphically demonstrated. Keywords: Dispersion parameter, variance function, Joint modelling of mean and dispersion

O transporte de grãos é de importância para a economia da Argentina. Atualmente, 84% dos grãos produzidos pelo país são transportados em rodovias, afetando sua competitividade devido a sua grande influencia nos custos.Nesse contexto, o presente trabalho tem como objetivo estudar a tomada de decisão de modo e destino dos consolidadores de grãos do Sul da Província de Buenos Aires. A partir de uma pesquisa de preferência declarada, conclui-se que a escolha de modo e destino é feita em conjunto. As variáveis relevantes para a escolha foram o preço FreeAlongsideShip no porto, o custo, a distância e a frequência do serviço. Os resultados estão em consonância com o encontrado na literatura, onde se destaca a modelagem conjunta e comportamental de diferentes etapas dos modelos de transporte e a inclusão de variáveis logísticas. Além disso, foram estimadas as elasticidades de cada alternativa e estudadas as curvas de iso-utilidade. Finalmente, foi realizada uma simulação de políticas de preço para a ferrovia, estudando a sua fatia de mercado, sua potencial arrecadação e o gasto total em transporte. / Agricultural trade is of great importance for Argentina. Nowadays, most of the crops transported by truck, affecting its competitivity because of its influence in direct costs. This study aims to analyze the choice process of the grain consolidatorsfromthe south of Buenos Aires province. From a stated preference survey, we conclude that the choice of mode and destination is made simultaneously. The relevant variables for the selection were the Free Alongside Ship price at the port, freight cost, distance and frequency. The results were consistent with those found in the literature, where behavioural joint modeling of different steps of transport models and the inclusion of logistics variables stand out. Moreover, price elasticities were estimated and iso-utility curves were studied. Finally, train price policies simulations were made observing market shares, expected incomes and total expenditures in transportation.

O transporte de grãos é de importância para a economia da Argentina. Atualmente, 84% dos grãos produzidos pelo país são transportados em rodovias, afetando sua competitividade devido a sua grande influencia nos custos.Nesse contexto, o presente trabalho tem como objetivo estudar a tomada de decisão de modo e destino dos consolidadores de grãos do Sul da Província de Buenos Aires. A partir de uma pesquisa de preferência declarada, conclui-se que a escolha de modo e destino é feita em conjunto. As variáveis relevantes para a escolha foram o preço FreeAlongsideShip no porto, o custo, a distância e a frequência do serviço. Os resultados estão em consonância com o encontrado na literatura, onde se destaca a modelagem conjunta e comportamental de diferentes etapas dos modelos de transporte e a inclusão de variáveis logísticas. Além disso, foram estimadas as elasticidades de cada alternativa e estudadas as curvas de iso-utilidade. Finalmente, foi realizada uma simulação de políticas de preço para a ferrovia, estudando a sua fatia de mercado, sua potencial arrecadação e o gasto total em transporte. / Agricultural trade is of great importance for Argentina. Nowadays, most of the crops transported by truck, affecting its competitivity because of its influence in direct costs. This study aims to analyze the choice process of the grain consolidatorsfromthe south of Buenos Aires province. From a stated preference survey, we conclude that the choice of mode and destination is made simultaneously. The relevant variables for the selection were the Free Alongside Ship price at the port, freight cost, distance and frequency. The results were consistent with those found in the literature, where behavioural joint modeling of different steps of transport models and the inclusion of logistics variables stand out. Moreover, price elasticities were estimated and iso-utility curves were studied. Finally, train price policies simulations were made observing market shares, expected incomes and total expenditures in transportation.

O transporte de grãos é de importância para a economia da Argentina. Atualmente, 84% dos grãos produzidos pelo país são transportados em rodovias, afetando sua competitividade devido a sua grande influencia nos custos.Nesse contexto, o presente trabalho tem como objetivo estudar a tomada de decisão de modo e destino dos consolidadores de grãos do Sul da Província de Buenos Aires. A partir de uma pesquisa de preferência declarada, conclui-se que a escolha de modo e destino é feita em conjunto. As variáveis relevantes para a escolha foram o preço FreeAlongsideShip no porto, o custo, a distância e a frequência do serviço. Os resultados estão em consonância com o encontrado na literatura, onde se destaca a modelagem conjunta e comportamental de diferentes etapas dos modelos de transporte e a inclusão de variáveis logísticas. Além disso, foram estimadas as elasticidades de cada alternativa e estudadas as curvas de iso-utilidade. Finalmente, foi realizada uma simulação de políticas de preço para a ferrovia, estudando a sua fatia de mercado, sua potencial arrecadação e o gasto total em transporte. / Agricultural trade is of great importance for Argentina. Nowadays, most of the crops transported by truck, affecting its competitivity because of its influence in direct costs. This study aims to analyze the choice process of the grain consolidatorsfromthe south of Buenos Aires province. From a stated preference survey, we conclude that the choice of mode and destination is made simultaneously. The relevant variables for the selection were the Free Alongside Ship price at the port, freight cost, distance and frequency. The results were consistent with those found in the literature, where behavioural joint modeling of different steps of transport models and the inclusion of logistics variables stand out. Moreover, price elasticities were estimated and iso-utility curves were studied. Finally, train price policies simulations were made observing market shares, expected incomes and total expenditures in transportation.

Abstract This thesis presents methods for modelling conditional variance and uncertainty of prediction at a query point on the basis of industrial process data. The introductory part of the thesis provides an extensive background of the examined methods and a summary of the results. The results are presented in detail in the original papers. The application presented in the thesis is modelling of the mean and variance of the mechanical properties of steel plates. Both the mean and variance of the mechanical properties depend on many process variables. A method for predicting the probability of rejection in a quali?cation test is presented and implemented in a tool developed for the planning of strength margins. The developed tool has been successfully utilised in the planning of mechanical properties in a steel plate mill. The methods for modelling the dependence of conditional variance on input variables are reviewed and their suitability for large industrial data sets are examined. In a comparative study, neural network modelling of the mean and dispersion narrowly performed the best. A method is presented for evaluating the uncertainty of regression-type prediction at a query point on the basis of predicted conditional variance, model variance and the effect of uncertainty about explanatory variables at early process stages. A method for measuring the uncertainty of prediction on the basis of the density of the data around the query point is proposed. The proposed distance measure is utilised in comparing the generalisation ability of models. The generalisation properties of the most important regression learning methods are studied and the results indicate that local methods and quadratic regression have a poor interpolation capability compared with multi-layer perceptron and Gaussian kernel support vector regression. The possibility of adaptively modelling a time-varying conditional variance function is disclosed. Two methods for adaptive modelling of the variance function are proposed. The background of the developed adaptive variance modelling methods is presented.

Cette thèse porte sur l’estimation spatiale de la teneur superficielle en carbone organiquedu sol ou teneur en SOC (pour ’Soil Organic Carbon content’), à l’échelle d’une petite région agricolefrancilienne. La variabilité de la teneur en SOC a été identifiée comme étant l’une des principales sourcesd’incertitude de la prédiction des stocks de SOC, dont l’accroissement favorise la fertilité des sols etl’atténuation des émissions de gaz à effet de serre. Nous utilisons des données provenant de sourceshétérogènes décrites selon différentes résolutions spatiales (prélèvements de sol, carte pédologique, imagessatellitaires multispectrales, etc) dans le but de produire d’une part une information spatiale exhaustive,et d’autre part des estimations précises de la teneur en SOC sur la région d’étude ainsi qu’une uneévaluation des incertitudes associées. Plusieurs modèles originaux, dont certains tiennent compte duchangement du support, sont construits et plusieurs approches et méthodes de prédiction sont considérées.Parmi elles, on retrouve des méthodes bayésiennes récentes et performantes permettant non seulementd’inférer des modèles sophistiqués intégrant conjointement des données de résolution spatiale différentemais aussi de traiter des données en grande dimension. Afin d’optimiser la qualité de la prédictiondes modélisations multi-sources, nous proposons également une approche efficace et rapide permettantd’accroître l’influence d’un type de données importantes mais sous-représentées dans l’ensemble de toutesles données initialement intégrées. / In this thesis, we are interested in the spatial estimation of the topsoil organic carbon(SOC) content over a small agricultural area located West of Paris. The variability of the SOC contenthas been identified as one of the main sources of prediction uncertainty of SOC stocks, whose increasepromotes soil fertility and mitigates greenhouse gas emissions. We use data issued from heterogeneoussources defined at different spatial resolutions (soil samples, soil map, multispectral satellite images, etc)with the aim of providing on the one hand an exhaustive spatial information, and on the other accurateestimates of the SOC content in the study region and an assessment of the related uncertainties. Severaloriginal models, some of which incorporate the change of support, are built and several approaches andprediction methods are considered. These include recent and powerful Bayesian methods enabling notonly the inference of sophisticated models integrating jointly data of different spatial resolutions butalso the exploitation of large data sets. In order to optimize the quality of prediction of the multi-sourcedata modellings, we also propose an efficient and fast approach : it allows to increase the influence of animportant but under-represented type of data, in the set of all initially integrated data.

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La prédiction d'un événement clinique à l'aide d'outils pronostiques est une question centrale en oncologie. L'émergence des biomarqueurs mesurés au cours du temps permet de proposer des outils incorporant les données répétées de ces biomarqueurs pour mieux guider le clinicien dans la prise en charge des patients. L'objectif de ce travail est de développer et valider des outils pronostiques dynamiques de rechute de cancer de la prostate, chez des patients traités initialement par radiothérapie externe, en prenant en compte les données répétées du PSA, l'antigène spécifique de la prostate, en plus des facteurs pronostiques standard. Ces outils sont dynamiques car ils peuvent être mis à jour à chaque nouvelle mesure disponible du biomarqueur. Ils sont construits à partir de modèles conjoints pour données longitudinales et de temps d'événement. Le principe de la modélisation conjointe est de décrire l'évolution du biomarqueur à travers un modèle linéaire mixte, décrire le risque d'événement à travers un modèle de survie et lier ces deux processus à travers une structure latente. Deux approches existent, les modèles conjoints à effets aléatoires partagés et les modèles conjoints à classes latentes. Dans un premier travail, nous avons tout d'abord comparé, en terme de qualité d'ajustement et de pouvoir prédictif, des modèles conjoints à effets aléatoires partagés différant par leur forme de dépendance entre le PSA et le risque de rechute clinique. Puis nous avons évalué et comparé ces deux approches de modélisation conjointe. Dans un deuxième travail, nous avons proposé un outil pronostique dynamique différentiel permettant d'évaluer le risque de rechute clinique suivant l'initiation ou non d'un second traitement (un traitement hormonal) au cours du suivi. Dans ces travaux, la validation de l'outil pronostique a été basée sur deux mesures de pouvoir prédictif: le score de Brier et l'entropie croisée pronostique. Dans un troisième travail, nous avons enfin décrit la dynamique des PSA après un second traitement de type hormonal chez des patients traités initialement par une radiothérapie seule. / The prediction of a clinical event with prognostic tools is a central issue in oncology. The emergence of biomarkers measured over time can provide tools incorporating repeated data of these biomarkers to better guide the clinician in the management of patients. The objective of this work is to develop and validate dynamic prognostic tools of recurrence of prostate cancer in patients initially treated by external beam radiation therapy, taking into account the repeated data of PSA, the Prostate-Specific Antigen, in addition to standard prognostic factors. These tools are dynamic because they can be updated at each available new measurement of the biomarker. They are built from joint models for longitudinal and time-to-event data. The principle of joint modelling is to describe the evolution of the biomarker through a linear mixed model, describe the risk of event through a survival model and link these two processes through a latent structure. Two approaches exist, shared random-effect models and joint latent class models. In a first study, we first compared in terms of goodness-of-fit and predictive accuracy shared random-effect models differing in the form of dependency between the PSA and the risk of clinical recurrence. Then we have evaluated and compared these two approaches of joint modelling. In a second study, we proposed a differential dynamic prognostic tool to evaluate the risk of clinical recurrence according to the initiation or not of a second treatment (an hormonal treatment) during the follow-up. In these works, validation of the prognostic tool was based on two measures of predictive accuracy: the Brier score and the prognostic cross-entropy. In a third study, we have described the PSA dynamics after a second treatment (hormonal) in patients initially treated by a radiation therapy alone.