This work is devoted to seeking methods for analysis of survival data with the Aalen model under special circumstances. We supposed, that all regression functions and all covariates of the observed individuals were nonnegative and we named this class of models monotone Aalen models. To find estimators of the unknown regres- sion functions we considered three maximum likelihood based approaches, namely the nonparametric maximum likelihood method, the Bayesian analysis using Beta processes as the priors for the unknown cumulative regression functions and the Bayesian analysis using a correlated prior approach, where the regression functions were supposed to be jump processes with a martingale structure.

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Le but de cette thèse est d’étudier l’approximation d’a priori impropres par des suites d’a priori propres. Nous définissons un mode de convergence sur les mesures de Radon strictement positives pour lequel une suite de mesures de probabilité peut admettre une mesure impropre pour limite. Ce mode de convergence, que nous appelons convergence q-vague, est indépendant du modèle statistique. Il permet de comprendre l’origine du paradoxe de Jeffreys-Lindley. Ensuite, nous nous intéressons à l’estimation de la taille d’une population. Nous considérons le modèle du removal sampling. Nous établissons des conditions nécessaires et suffisantes sur un certain type d’a priori pour obtenir des estimateurs a posteriori bien définis. Enfin, nous montrons à l’aide de la convergence q-vague, que l’utilisation d’a priori vagues n’est pas adaptée car les estimateurs obtenus montrent une grande dépendance aux hyperparamètres. / The purpose of this thesis is to study the approximation of improper priors by proper priors. We define a convergence mode on the positive Radon measures for which a sequence of probability measures could converge to an improper limiting measure. This convergence mode, called q-vague convergence, is independant from the statistical model. It explains the origin of the Jeffreys-Lindley paradox. Then, we focus on the estimation of the size of a population. We consider the removal sampling model. We give necessary and sufficient conditions on the hyperparameters in order to have proper posterior distributions and well define estimate of abundance. In the light of the q-vague convergence, we show that the use of vague priors is not appropriate in removal sampling since the estimates obtained depend crucially on hyperparameters.

Esta dissertação de mestrado tem como objeto de estudo o fenômeno conhecido como antonismo, nome dado ao movimento de apoio à reivindicação de D. Antônio, prior do Crato (1531-1595), à coroa portuguesa após a morte de D. Sebastião (1555-1578). A luta de D. Antônio e dos antonistas pelo trono foi assunto de controvérsia e polêmica na historiografia, ora compreendido como um surto patriótico, ora como uma revolta popular, mas sempre circunscrito aos eventos da crise dinástica. Nesta dissertação, buscaremos demonstrar que este fenômeno corresponde a uma linha de força interna da política portuguesa quinhentista, que tem origem nas disputas e conflitos entre o infante D. Luís e D. João III e de diversas facções descontentes com a política do reino que aos poucos construíram a pretensão de D. Antônio, prior do Crato, à coroa portuguesa e, portanto, sendo uma possibilidade política concreta antes e depois da crise dinástica portuguesa (1578-1581). / This dissertation has as its object of study the phenomenon known as antonismo, name given to the movement to support the claim D. Antônio, prior of Crato (1531-1595), to the Portuguese crown after the death of D. Sebastião (1555-1578). The struggle of D. Antônio and the antonistas for the throne was the subject of dispute and controversy in historiography, now understood as a patriotic outbreak, now as a popular revolt, but always limited to the events of dynastic crisis. This dissertation demonstrates that this phenomenon corresponds to an inner power line of the sixteenth-century Portuguese policy, which has its origins in disputes and conflicts between the infante D. Luís and D. João III and from various factions discontented with the policy of the kingdom that gradually built up the pretense of D. Antônio, prior of Crato, to the Portuguese crown, and thus being a real political possibility before and after the Portuguese dynastic crisis (1578-1581).

Esta dissertação de mestrado tem como objeto de estudo o fenômeno conhecido como antonismo, nome dado ao movimento de apoio à reivindicação de D. Antônio, prior do Crato (1531-1595), à coroa portuguesa após a morte de D. Sebastião (1555-1578). A luta de D. Antônio e dos antonistas pelo trono foi assunto de controvérsia e polêmica na historiografia, ora compreendido como um surto patriótico, ora como uma revolta popular, mas sempre circunscrito aos eventos da crise dinástica. Nesta dissertação, buscaremos demonstrar que este fenômeno corresponde a uma linha de força interna da política portuguesa quinhentista, que tem origem nas disputas e conflitos entre o infante D. Luís e D. João III e de diversas facções descontentes com a política do reino que aos poucos construíram a pretensão de D. Antônio, prior do Crato, à coroa portuguesa e, portanto, sendo uma possibilidade política concreta antes e depois da crise dinástica portuguesa (1578-1581). / This dissertation has as its object of study the phenomenon known as antonismo, name given to the movement to support the claim D. Antônio, prior of Crato (1531-1595), to the Portuguese crown after the death of D. Sebastião (1555-1578). The struggle of D. Antônio and the antonistas for the throne was the subject of dispute and controversy in historiography, now understood as a patriotic outbreak, now as a popular revolt, but always limited to the events of dynastic crisis. This dissertation demonstrates that this phenomenon corresponds to an inner power line of the sixteenth-century Portuguese policy, which has its origins in disputes and conflicts between the infante D. Luís and D. João III and from various factions discontented with the policy of the kingdom that gradually built up the pretense of D. Antônio, prior of Crato, to the Portuguese crown, and thus being a real political possibility before and after the Portuguese dynastic crisis (1578-1581).

Cette dissertation traite des trois thématiques suivantes : incertitude, fonctions d’utilité et non-arbitrage. Dans le premier chapitre, nous supposons qu’il n’y a pas d’incertitude sur les croyances et établissons l’existence d’un portefeuille optimal pour un investisseur qui opère dans un marché financier multi-période à temps discret et maximise son espérance terminale d’utilité. Nous considérons des fonctions d’utilité aléatoires non concaves, non continues définies sur l’axe réel positif. La preuve repose sur de la programmation dynamique et des outils de théorie de la mesure.Dans les trois chapitres suivant nous introduisons le concept d’incertitude knightienne et adoptons le modèle de marché financier multi-période à temps discret avec croyances multiples non dominées introduit par B. Bouchard and M. Nutz (Arbitrage and duality in nondominated discrete-time models)Dans le second chapitre, nous étudions la notion de non-arbitrage quasi-sûre introduite par B. Bouchard and M. Nutz (Arbitrage and duality in nondominated discrete-time models) et en proposons deux formulations équivalentes: une version quantitative et une version géométrique. Nous proposons aussi une condition forte de non-arbitrage afin de simplifier des difficultés techniques.Nous utilisons ces résultats dans le troisième chapitre pour résoudre le problème de la maximisation d’espérance d’utilité sous la plus défavorable des croyances pour des fonctions d’utilité concaves, définies sur l’axe positif réel non-bornées. La preuve utilise à nouveau de la programmation dynamique et des techniques de sélection mesurable.Finalement, dans le dernier chapitre, nous développons un modèle de d’évaluation par indifférence d’utilité et démontrons que sous de bonnes conditions, le prix d’indifférence d’un actif contingent converge vers son prix de sur réplication. / This dissertation evolves around the following three general thematic: uncertainty, utility and no-arbitrage.In the first chapter we establish the existence of an optimal portfolio for investor trading in a multi-period and discrete-time financial market without uncertainty and maximising its terminal wealth expected utility. We consider general non-concave and non-smooth random utility function defined on the half real-line. The proof is based on dynamic programming and measure theory tools.In the next three chapters, we introduce the concept of Knightian uncertainty and adopt the multi-prior non dominated and discrete time framework introduced in [25]..In this setting, in the second chapter we study the notion of quasi-sure no-arbitrage introduced in [25] and propose two equivalent definitions: a quantitative and geometric characterisation. We also introduce a stronger no-arbitrage condition that simplifies some of the measurability difficulties.In the third chapter, we build on the results obtained in the previous chapter to study the maximisation of multiple-priors non-dominated worst-case expected utility for investors trading in a multi-period and discrete-time financial for general concave utility functions defined on the half-real line unbounded from above. The proof uses again a dynamic programming framework together with measurable selection.Finally the last chapter formulates a utility indifference pricing model for investor trading in a multi-period and discrete-time financial market. We prove that under suitable condition the multiples-priors utility indifference prices of a contingent claim converge to its multiple-priors superreplication price

La modélisation de la dynamique des populations de thons et grands pélagiques pour l'évaluation des stocks est confrontée à deux enjeux majeurs. (1) L'hypothèse forte de proportionnalité entre Captures Par Unité d'Effort de pêche (CPUE) et l'abondance des stocks. Les CPUE des pêcheries commerciales sont en effet les seules mesures relatives de biomasse utilisées pour l'évaluations des stocks de thons et grands pélagiques, malgré leur manque de représentativité de l'abondance de ces populations. (2) Le manque de données informatives pour modéliser la relation Stock-Recrutement (SR) ce qui conduit à utiliser des contraintes sur la "steepness" de cette fonction. Nous examinons comment l'introduction d'informations indépendantes des pêcheries commerciales dans les modèles pour l'évaluation des stocks thoniers permet de lever l'hypothèse de capturabilité constante et de mieux justifier le choix de la steepness de la relation SR. Le cadre statistique bayésien autorise la prise en compte d'informations supplémentaires via des distributions a priori informatives (priors). Cette thèse examine donc les possibilités d'élicitation de priors informatifs pour des paramètres démographiques et des paramètres liés à la capturabilité des engins de pêche, ainsi que l'utilisation de ces priors dans un modèle global. Les cas d'études sont les stocks de thon rouge (Thunnus thynnus) et d'albacore (Thunnus albacares) de l'Atlantique. La grande variabilité naturelle des taux de mortalités pré-recrutement pose des limites à l'utilisation des seuls traits d'histoire de vie pour l'élicitation de priors pour des paramètres démographiques. Par ailleurs, la relation SR pour les thonidés est remise en question par une valeur de steepness proche de 1. Il apparait que des priors informatifs sur la capturabilité dans un modèle hiérarchique global permettent de réduire les incertitudes dans le diagnostic sur l'état d'un stock thonier. Nous montrons ainsi que le diagnostic sur le stock Atlantique d'albacore est plus pessimiste qu'attendu la tendance à la hausse des capturabilités des principaux engins de pêche est prise en compte. L'élicitation de priors présente donc un fort intérêt pour utiliser des informations supplémentaires et extérieures aux CPUE et améliorer la perception de l'état des stock thoniers. / Modelisation of the population dynamics of tunas and tuna like species for stock assessment is facing two issues. (1) The hypothesis of proportionality between Catch Per Unit Effort (CPUE) and abundance (constant catchability). CPUEs from commercial fisheries appear to be the only relative measure of abundance in spite of their lack of representativity of the abundances of the populations. (2) The lack of informative data for the modelisation of the Stock-Recruit (SR) relationship, which leads to constraint this function on its steepness. The introduction of fisheries-independent sources of information is investigated in order to relax the assumption of constant catchability and to provide better justification of steepness choice for the SR relationship. The Bayesian statistical framework allows the consideration of additional information a priori via informative distributions (priors). This work investigate the elicitation of informative priors for demographic parameters and parameters related to the catchability of fishing gear, as well as the use of these priors into a surplus production model. The cases of the Atlantic bluefin tuna (Thunnus thynnus) and of the yellowfin tuna (Thunnus albacares}) were taken as examples. The large natural variability of pre-recruits mortality rates limits the use of life history traits for eliciting priors for demographic parameters. In addition, the SR relationship for tuna is challenged by a steepness value close to 1. It appears that informative priors on catchability parameters, in a hierarchical surplus production model, reduce uncertainties in the diagnosis on the status of tuna stocks. We show that the status of the Atlantic yellowfin tuna stock is more critical taking into account upward trends in the main fishing gears catchabilities. We conclude that prior elicitation is a reliable tool to take into account additionnal information and to improve tunas stock assessment.

Magister Artium - MA / This research paper investigates the extent to which the Recognition of Prior Learning (RPL) is implemented in the Real Estate industry within the Johannesburg Metropolitan area. The Real Estate industry is an ideal industry to assess the prior learning of real estate agents since there is no doubt that such a workplace has been recognized as an effective and efficient learning environment which allows workers to take part in an ever-changing work environment (Le Clus, 2011). Despite the availability of resources from different entities, i.e. the Services Sector Education and Training Authority (SETA), RPL centres, Umalusi, the Department of Higher Education and Training (DHET), the Estate Agency Affairs Board (EAAB), and so on (OECD, 2010) there seems to be incompatibility between the existing policy and the implementation of such policy in the Real Estate industry. Hence, to paraphrase a common theme within the literature (Cameron and Miller, 2004) there is a gap between the promise and rhetoric of RPL and the actual reality, and a disjuncture between policy formulation and implementation of RPL. Also, most research (Cameron and Miller, 2004) reveals that RPL has neither fulfilled its promised potential of encouraging the previously disadvantaged groups to access formal education and training, nor achieved its goal as a mechanism for social inclusion. The two primary research questions for this research paper were: Why are potential RPL candidates not taking the RPL route to obtain their certification? What are the barriers that obstruct efficient RPL implementation within the Real Estate industry? The research design was exploratory within a qualitative framework employing focus group interviewing, individual interviewing and the distribution of questionnaires that consisted of open-ended questions. The research sample comprised nineteen participants that included eight estate agents, four principals, five RPL Centers‟ representatives, one representative from the Services SETA and one representative from the Estate Agency Affairs Board. Master of Education in Adult Education and Global Change - Dissertation [University of the Western Cape] The research findings show that there are serious issues with the implementation current RPL policy within the real estate industry. Many scholars (Colardyn and Bjørna°vold, 2004; Bjørna°vold, 2000) indicate that RPL comes with its challenges, for instance that of the role it can play and the extent to which it can address the twin goals of increasing educational level of participation and employment rates. RPL also takes much time, as Anderson, Fejes and Ahn (2004) stress, to transform non-formal and informal learning into more or less formal learning that is ratified in the form of officially acknowledged certificates. Elements such as lack of or insufficient learner support by advisors and language barriers, have contributed significantly to the dropping out of most candidates. The strength of RPL is that unaccredited knowledge and skills can be brought into the open for everyone to see and, in a sense, come into use (Berglund and Anderson, 2012). This was made evident by the candidates who made it through RPL. RPL has also contributed to social equity and redress by admitting candidates as recognised agents and principals who previously were about to be excluded from the industry due to lack of recognised qualifications.

L’une des grandes applications de la statistique est la validation et la comparaison de modèles probabilistes au vu des données. Cette branche des statistiques a été développée depuis la formalisation de la fin du 19ième siècle par des pionniers comme Gosset, Pearson et Fisher. Dans le cas particulier de l’approche bayésienne, la solution à la comparaison de modèles est le facteur de Bayes, rapport des vraisemblances marginales, quelque soit le modèle évalué. Cette solution est obtenue par un raisonnement mathématique fondé sur une fonction de coût.Ce facteur de Bayes pose cependant problème et ce pour deux raisons. D’une part, le facteur de Bayes est très peu utilisé du fait d’une forte dépendance à la loi a priori (ou de manière équivalente du fait d’une absence de calibration absolue). Néanmoins la sélection d’une loi a priori a un rôle vital dans la statistique bayésienne et par conséquent l’une des difficultés avec la version traditionnelle de l’approche bayésienne est la discontinuité de l’utilisation des lois a priori impropres car ils ne sont pas justifiées dans la plupart des situations de test. La première partie de cette thèse traite d’un examen général sur les lois a priori non informatives, de leurs caractéristiques et montre la stabilité globale des distributions a posteriori en réévaluant les exemples de [Seaman III 2012]. Le second problème, indépendant, est que le facteur de Bayes est difficile à calculer à l’exception des cas les plus simples (lois conjuguées). Une branche des statistiques computationnelles s’est donc attachée à résoudre ce problème, avec des solutions empruntant à la physique statistique comme la méthode du path sampling de [Gelman 1998] et à la théorie du signal. Les solutions existantes ne sont cependant pas universelles et une réévaluation de ces méthodes suivie du développement de méthodes alternatives constitue une partie de la thèse. Nous considérons donc un nouveau paradigme pour les tests bayésiens d’hypothèses et la comparaison de modèles bayésiens en définissant une alternative à la construction traditionnelle de probabilités a posteriori qu’une hypothèse est vraie ou que les données proviennent d’un modèle spécifique. Cette méthode se fonde sur l’examen des modèles en compétition en tant que composants d’un modèle de mélange. En remplaçant le problème de test original avec une estimation qui se concentre sur le poids de probabilité d’un modèle donné dans un modèle de mélange, nous analysons la sensibilité sur la distribution a posteriori conséquente des poids pour divers modélisation préalables sur les poids et soulignons qu’un intérêt important de l’utilisation de cette perspective est que les lois a priori impropres génériques sont acceptables, tout en ne mettant pas en péril la convergence. Pour cela, les méthodes MCMC comme l’algorithme de Metropolis-Hastings et l’échantillonneur de Gibbs et des approximations de la probabilité par des méthodes empiriques sont utilisées. Une autre caractéristique de cette variante facilement mise en œuvre est que les vitesses de convergence de la partie postérieure de la moyenne du poids et de probabilité a posteriori correspondant sont assez similaires à la solution bayésienne classique / One of the major applications of statistics is the validation and comparing probabilistic models given the data. This branch statistics has been developed since the formalization of the late 19th century by pioneers like Gosset, Pearson and Fisher. In the special case of the Bayesian approach, the comparison solution of models is the Bayes factor, ratio of marginal likelihoods, whatever the estimated model. This solution is obtained by a mathematical reasoning based on a loss function. Despite a frequent use of Bayes factor and its equivalent, the posterior probability of models, by the Bayesian community, it is however problematic in some cases. First, this rule is highly dependent on the prior modeling even with large datasets and as the selection of a prior density has a vital role in Bayesian statistics, one of difficulties with the traditional handling of Bayesian tests is a discontinuity in the use of improper priors since they are not justified in most testing situations. The first part of this thesis deals with a general review on non-informative priors, their features and demonstrating the overall stability of posterior distributions by reassessing examples of [Seaman III 2012].Beside that, Bayes factors are difficult to calculate except in the simplest cases (conjugate distributions). A branch of computational statistics has therefore emerged to resolve this problem with solutions borrowing from statistical physics as the path sampling method of [Gelman 1998] and from signal processing. The existing solutions are not, however, universal and a reassessment of the methods followed by alternative methods is a part of the thesis. We therefore consider a novel paradigm for Bayesian testing of hypotheses and Bayesian model comparison. The idea is to define an alternative to the traditional construction of posterior probabilities that a given hypothesis is true or that the data originates from a specific model which is based on considering the models under comparison as components of a mixture model. By replacing the original testing problem with an estimation version that focus on the probability weight of a given model within a mixture model, we analyze the sensitivity on the resulting posterior distribution of the weights for various prior modelings on the weights and stress that a major appeal in using this novel perspective is that generic improper priors are acceptable, while not putting convergence in jeopardy. MCMC methods like Metropolis-Hastings algorithm and the Gibbs sampler are used. From a computational viewpoint, another feature of this easily implemented alternative to the classical Bayesian solution is that the speeds of convergence of the posterior mean of the weight and of the corresponding posterior probability are quite similar.In the last part of the thesis we construct a reference Bayesian analysis of mixtures of Gaussian distributions by creating a new parameterization centered on the mean and variance of those models itself. This enables us to develop a genuine non-informative prior for Gaussian mixtures with an arbitrary number of components. We demonstrate that the posterior distribution associated with this prior is almost surely proper and provide MCMC implementations that exhibit the expected component exchangeability. The analyses are based on MCMC methods as the Metropolis-within-Gibbs algorithm, adaptive MCMC and the Parallel tempering algorithm. This part of the thesis is followed by the description of R package named Ultimixt which implements a generic reference Bayesian analysis of unidimensional mixtures of Gaussian distributions obtained by a location-scale parameterization of the model. This package can be applied to produce a Bayesian analysis of Gaussian mixtures with an arbitrary number of components, with no need to specify the prior distribution.

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