Yes / Many studies have examined the extent to which individuals’ probability judgments depart from Bayes’ theorem when revising probability estimates in the light of new information. Generally, these studies have not considered the implications of such departures for decisions involving risk. We identify when such departures will occur in two common types of decisions. We then report on two experiments where people were asked to revise their own prior probabilities of a forthcoming economic recession in the light of new information. When the reliability of the new information was independent of the state of nature, people tended to overreact to it if their prior probability was low and underreact if it was high. When it was not independent, they tended to display conservatism. We identify the circumstances where discrepancies in decisions arising from a failure to use Bayes’ theorem were most likely to occur in the decision context we examined. We found that these discrepancies were relatively rare and, typically, were not serious.

La science des réseaux est notamment à la recherche de modèles mathématiques capables de reproduire le comportement de systèmes complexes empiriques. Cependant, la représentation usuelle, le graphe, est parfois inadéquate étant donné sa limitation à encoder uniquement les relations par paires. De nombreux travaux récents suggèrent que l'utilisation de l'hypergraphe, une généralisation décrivant les interactions d'ordre supérieur (plus de deux composantes), permet d'expliquer des phénomènes auparavant incompris avec le graphe. Or, la structure de ces réseaux complexes est rarement ou difficilement observée directement. De fait, on mesure plutôt une quantité intermédiaire, comme la fréquence de chaque interaction, pour ensuite reconstruire la structure originale. Bien que de nombreuses méthodes de reconstruction de graphes aient été développées, peu d'approches permettent de retrouver les interactions d'ordre supérieur d'un système complexe. Dans ce mémoire, on développe une nouvelle approche de reconstruction pouvant déceler les interactions connectant trois noeuds parmi des observations dyadiques bruitées. Basée sur l'inférence bayésienne, cette méthode génère la distribution des hypergraphes les plus plausibles pour un jeu de données grâce à un algorithme de type Metropolis-Hastings-within-Gibbs, une méthode de Monte-Carlo par chaînes de Markov. En vue d'évaluer la pertinence d'un modèle d'interactions d'ordre supérieur pour des observations dyadiques, le modèle d'hypergraphe développé est comparé à un second modèle bayésien supposant que la structure sous-jacente est un graphe admettant deux types d'interactions par paires. Les résultats obtenus pour des hypergraphes synthétiques et empiriques indiquent que la corrélation intrinsèque à la projection d'interactions d'ordre supérieur améliore le processus de reconstruction lorsque les observations associées aux interactions dyadiques et triadiques sont semblables. / Network science is looking for mathematical models capable of reproducing the behavior of empirical complex systems. However, the usual representation, the graph, is sometimes inadequate given its limitation to encode only pairwise relationships. Many recent works suggest that the use of the hypergraph, a generalization describing higher-order interactions (more than two components), allows to explain phenomena previously not understood with graphs. However, the structure of these complex networks is seldom or hardly observed directly. Instead, we measure an intermediate quantity, such as the frequency of each interaction, and then reconstruct the original structure. Although many graph reconstruction methods have been developed, few approaches recover the higher-order interactions of a complex system. In this thesis, we develop a new reconstruction approach which detects interactions connecting three vertices among noisy dyadic observations. Based on Bayesian inference, this method generates the distribution of the most plausible hypergraphs for a dataset using a Metropolis-Hastings-within-Gibbs algorithm, a Markov chain Monte Carlo method. In order to evaluate the relevance of a higher-order interaction model for dyadic observations, the developed hypergraph model is compared to a second Bayesian model assuming that the underlying structure is a graph admitting two types of pairwise interactions. Results for synthetic and empirical hypergraphs indicate that the intrinsic correlation to the projection of higher-order interactions improves the reconstruction process when observations associated with dyadic and triadic interactions are similar.

This paper explores the fit of a stochastic volatility model, in which the Box-Cox transformation of the squared volatility follows an autoregressive Gaussian distribution, to the continuously compounded daily returns of the Australian stock index. Estimation was difficult, and over-fitting likely, because more variables are present than data. We developed a revised model that held a couple of these variables fixed and then, further, a model which reduced the number of variables significantly by grouping trading days. A Metropolis-Hastings algorithm was used to simulate the joint density and derive estimated volatilities. Though autocorrelations were higher with a smaller Box-Cox transformation parameter, the fit of the distribution was much better.

OBJETIVO: Comparar a eficácia e a tolerabilidade dos fármacos antiepiléticos (FAE) no tratamento em monoterapia de pacientes com epilepsia focal ou generalizada. MÉTODOS: Uma revisão sistemática foi realizada por meio da busca nas bases de dados eletrônicas Pubmed, Scopus, Web of Science e Cochrane Register of Controlled Trials. Foram incluídos os ensaios clínicos controlados com pacientes com epilepsia, em tratamento com FAE, via oral, em monoterapia, e que avaliaram o número de pacientes que atingiram a remissão das crises epilépticas, que interromperam o tratamento devido à ineficácia terapêutica ou à ocorrência de reações adversas (RAM) intoleráveis. Meta-análises de comparação de múltiplos tratamentos foram realizadas por meio do modelo bayesiano de efeitos randômicos que permitiu o cálculo do Odds Ratio meta-analítico para os FAE estudados. Também foi realizado um ranqueamento da probabilidade de cada FAE ser a melhor opção em eficácia e tolerabilidade. RESULTADOS E CONCLUSÕES: A busca identificou 18874 publicações, no entanto apenas 71 estudos foram selecionados, compreendendo 17555 pacientes com epilepsia. Vinte e nove estudos apresentaram os desfechos de eficácia no tratamento de crises focais, 19 em crises generalizadas e 58 apresentaram dados de tolerabilidade. Nesses estudos, 15 FAE foram avaliados. No tratamento das crises focais, os FAE de nova geração levetiracetam (LEV), lamotrigina (LTG), oxcarbazepina, sultiame e topiramato (TPM) demonstraram possuir eficácia equivalente à carbamazepina (CBZ), clobazam e valproato (VPA). No entanto, a CBZ apresentou o pior perfil de tolerabilidade devido à grande probabilidade do paciente abandonar o tratamento devido à RAM intoleráveis. Quanto ao tratamento das crises generalizadas, a LTG, LEV e TPM são tão eficazes quanto o VPA para o tratamento de crises generalizadas tônico-clônicas, tônicas e clônicas. O VPA e a etosuximida constituem as melhores opções para o tratamento de crises de ausências, enquanto que a LTG mostrou-se menos eficaz. Para o tratamento de crises mioclônicas e espasmos infantis mais ensaios clínicos randomizados são necessários para fornecer boas evidências que possam guiar a decisão clínica dos profissionais de saúde. Dentre os FAE com perfil de eficácia adequado, a LTG destacou-se pela menor probabilidade de manifestar RAM intoleráveis. / OBJECTIVE: To compare the efficacy and tolerability of the antiepileptic drugs (AED) in monotherapy of patients with focal or generalized epilepsy. METHODS: A systematic review was in the Medline/Pubmed, Scopus, Web of Science and Cochrane Register of Controlled Trials databases. We included randomized clinical trials of patients with epilepsy treated with oral monotherapy AED, which evaluated number of patients becoming seizure free at the maintenance treatment period; number of patients which withdrawals from the study because of therapeutic inefficacy and number of patients which withdrawals from the study because of intolerable adverse reaction. Network meta-analyses were performed using Bayesian random effects model. We also carried out a ranking of the probability of each AED be the best option in the efficacy and tolerability outcomes. Sensitivity analyses were conducted in order to check the robustness of the results. RESULTS AND CONCLUSIONS: The research identified 18,874 publications, but only 71 studies were selected, comprising 17555 patients with epilepsy.Twenty-nine trials showed the efficacy outcomes in the treatment of focal seizures, 19 in generalized seizures and 58 showed tolerability data. In the treatment of focal seizures, levetiracetam (LEV), lamotrigine (LTG), oxcarbazepine, sultiame and topiramate (TPM) have demonstrated equivalent efficacy to carbamazepine (CBZ), clobazam and valproate (VPA). LTG, LEV and TPM are as effective as the VPA for the treatment of generalized tonic-clonic, tonic and clonic seizures. VPA and ethosuximide are the best options for the treatment of absence seizures, whereas LTG was less effective. For the treatment of myoclonic seizures and infantile spasms, more randomized clinical trials are needed to provide good evidence to guide the clinical decision of health professionals. Among the AED with adequate efficacy profile, LTG stands out as the AED with the best tolerability profile, suggesting it may be the best option for the treatment of patients with epilepsy.

A maioria dos textos na literatura de testes de hipóteses trata de critérios de otimalidade para um determinado problema de decisão. No entanto, existem, em menor quantidade, alguns textos sobre os problemas de se realizar testes de hipóteses simultâneos e sobre a concordância lógica de suas soluções ótimas. Algo que se espera de testes de hipóteses simultâneos e que, se uma hipótese H1 implica uma hipótese H0, então é desejável que a rejeição da hipótese H0 necessariamente implique na rejeição da hipótese H1, para uma mesma amostra observada. Essa propriedade é chamada aqui de monotonicidade. A fim de estudar essa propriedade sob um ponto de vista mais geral, neste trabalho é definida a nocão de classe de testes de hipóteses, que estende a funcão de teste para uma sigma-álgebra de possíveis hipóteses nulas, e introduzida uma definição de monotonicidade. Também é mostrado, por meio de alguns exemplos simples, que, para um nível de signicância fixado, a classe de testes Razão de Verossimilhanças Generalizada (RVG) não apresenta monotonicidade, ao contrário de testes formulados sob a perspectiva bayesiana, como o teste de Bayes baseado em probabilidades a posteriori, o teste de Lindley e o FBST. Porém, são verificadas, sob a teoria da decisão, quando possível, quais as condições suficientes para que uma classe de testes de hipóteses tenha monotonicidade. / Most of the texts in the literature of hypothesis testing deal with optimality criteria for a single decision problem. However, there are, to a lesser extent, texts on the problem of simultaneous hypothesis testing and the logical consistency of the optimal solutions of such procedures. For instance, the following property should be observed in simultaneous hypothesis testing: if a hypothesis H implies a hypothesis H0, then, on the basis of the same sample observation, the rejection of the hypothesis H0 necessarily should imply the rejection of the hypothesis H. Here, this property is called monotonicity. To investigate this property under a more general point of view, in this work, it is dened rst the notion of a class of hypothesis testing, which extends the test function to a sigma-eld of possible null hypotheses, and then the concept of monotonicity is introduced properly. It is also shown, through some simple examples, that for a xed signicance level, the class of Generalized Likelihood Ratio tests (GLR) does not meet monotonicity, as opposed to tests developed under the Bayesian perspective, such as Bayes tests based on posterior probabilities, Lindleys tests and Full Bayesian Signicance Tests (FBST). Finally, sucient conditions for a class of hypothesis testing to have monotonicity are determined, when possible, under a decision-theoretic approach.

O estudo de sistemas complexos nos ajuda a entender como regras locais simples podem gerar padrões agregados complexos e muitas vezes inesperados. Quando as regras são bem definidas e os padrões observáveis, o sistema pode ser modelado e seus resultados comparados. Um dos maiores desafios para a modelagem de sistemas complexos é definir a regra de interação responsável pelo comportamento complexo. Em dinâmica de opiniões, padrão complexo e inesperado pode ser o súbito consenso ou até mesmo a polarização, e objetivo, então, se torna verificar em que circunstâncias podemos observar pessoas concordarem ou descordarem. Embora haja uma série de modelos de dinâmica de opiniões para descrever como as pessoas interagem, cada um define a regra de formação da opinião de forma ad hoc. O modelo CODA (Continuous opinions and Discret Actions) propõe uma fundamentação teórica para os modelos de dinâmica de opiniões baseada em teoria de probabilidade. Suas aplicações se estendem desde estudos sobre inovação à epistemologia. Nesta dissertação, aprofundamos os estudos de epistemologia que envolvem o CODA, investigando principalmente o efeito da confiança no processo de confirmação cientifica. Nossas simulações corroboram investigações sociológicas e históricas sobre o papel fundamental da confiança no processo de aquisição e geração do conhecimento / The study of complex systems helps us understand how simple local rules can generate complex and often unexpected aggregate patterns. When the rules are well defined and patterns observed, the system can be modeled and its results compared. One of the major challenges for modeling complex systems is to define a rule of interaction responsible for complex behavior. In opinion dynamics, complex and unexpected pattern may be the sudden consensus or even a polarization, so the aim it is to verify under what circumstances we can observe agreement or disagreement. Although there are a number of models of opinion dynamics to describe how people should interact with each other, each one defines an ad hoc opinion formation rule. The model of opinion dynamics CODA (Continuous Opinions and Discret Actions) proposes a theoretical framework for the models of opinion dynamics, based on probability theory. Their applications range from studies on innovation to epistemology. In this dissertation, we deepen the studies of epistemology that involve the CODA, investigating mainly the effect of the trust in the process of scientific confirmation. Our simulations corroborates sociological and historical researches on the role of trust in the process of acquisition and generation of knowledge

O estudo de sistemas complexos nos ajuda a entender como regras locais simples podem gerar padrões agregados complexos e muitas vezes inesperados. Quando as regras são bem definidas e os padrões observáveis, o sistema pode ser modelado e seus resultados comparados. Um dos maiores desafios para a modelagem de sistemas complexos é definir a regra de interação responsável pelo comportamento complexo. Em dinâmica de opiniões, padrão complexo e inesperado pode ser o súbito consenso ou até mesmo a polarização, e objetivo, então, se torna verificar em que circunstâncias podemos observar pessoas concordarem ou descordarem. Embora haja uma série de modelos de dinâmica de opiniões para descrever como as pessoas interagem, cada um define a regra de formação da opinião de forma ad hoc. O modelo CODA (Continuous opinions and Discret Actions) propõe uma fundamentação teórica para os modelos de dinâmica de opiniões baseada em teoria de probabilidade. Suas aplicações se estendem desde estudos sobre inovação à epistemologia. Nesta dissertação, aprofundamos os estudos de epistemologia que envolvem o CODA, investigando principalmente o efeito da confiança no processo de confirmação cientifica. Nossas simulações corroboram investigações sociológicas e históricas sobre o papel fundamental da confiança no processo de aquisição e geração do conhecimento / The study of complex systems helps us understand how simple local rules can generate complex and often unexpected aggregate patterns. When the rules are well defined and patterns observed, the system can be modeled and its results compared. One of the major challenges for modeling complex systems is to define a rule of interaction responsible for complex behavior. In opinion dynamics, complex and unexpected pattern may be the sudden consensus or even a polarization, so the aim it is to verify under what circumstances we can observe agreement or disagreement. Although there are a number of models of opinion dynamics to describe how people should interact with each other, each one defines an ad hoc opinion formation rule. The model of opinion dynamics CODA (Continuous Opinions and Discret Actions) proposes a theoretical framework for the models of opinion dynamics, based on probability theory. Their applications range from studies on innovation to epistemology. In this dissertation, we deepen the studies of epistemology that involve the CODA, investigating mainly the effect of the trust in the process of scientific confirmation. Our simulations corroborates sociological and historical researches on the role of trust in the process of acquisition and generation of knowledge

Ce travail est dédié à la résolution de plusieurs problèmes de grand intérêt en traitement d’images : segmentation, choix de modèle et estimation de paramètres, pour le cas spécifique d’images texturées indirectement observées (convoluées et bruitées). Dans ce contexte, les contributions de cette thèse portent sur trois plans différents : modéle, méthode et algorithmique.Du point de vue modélisation de la texture, un nouveaumodèle non-gaussien est proposé. Ce modèle est défini dans le domaine de Fourier et consiste en un mélange de Gaussiennes avec une Densité Spectrale de Puissance paramétrique.Du point de vueméthodologique, la contribution est triple –troisméthodes Bayésiennes pour résoudre de manière :–optimale–non-supervisée–des problèmes inverses en imagerie dans le contexte d’images texturées ndirectement observées, problèmes pas abordés dans la littérature jusqu’à présent.Plus spécifiquement,1. la première méthode réalise la déconvolution myope non-supervisée et l’estimation des paramètres de la texture,2. la deuxième méthode est dédiée à la déconvolution non-supervisée, le choix de modèle et l’estimation des paramètres de la texture et, finalement,3. la troisième méthode déconvolue et segmente une image composée de plusieurs régions texturées, en estimant au même temps les hyperparamètres (niveau du signal et niveau du bruit) et les paramètres de chaque texture.La contribution sur le plan algorithmique est représentée par une nouvelle version rapide de l’algorithme Metropolis-Hastings. Cet algorithme est basé sur une loi de proposition directionnelle contenant le terme de la ”direction de Newton”. Ce terme permet une exploration rapide et efficace de l’espace des paramètres et, de ce fait, accélère la convergence. / This thesis is addressing a series of inverse problems of major importance in the fieldof image processing (image segmentation, model choice, parameter estimation, deconvolution)in the context of textured images. In all of the aforementioned problems theobservations are indirect, i.e., the textured images are affected by a blur and by noise. Thecontributions of this work belong to three main classes: modeling, methodological andalgorithmic. From the modeling standpoint, the contribution consists in the development of a newnon-Gaussian model for textures. The Fourier coefficients of the textured images are modeledby a Scale Mixture of Gaussians Random Field. The Power Spectral Density of thetexture has a parametric form, driven by a set of parameters that encode the texture characteristics.The methodological contribution is threefold and consists in solving three image processingproblems that have not been tackled so far in the context of indirect observationsof textured images. All the proposed methods are Bayesian and are based on the exploitingthe information encoded in the a posteriori law. The first method that is proposed is devotedto the myopic deconvolution of a textured image and the estimation of its parameters.The second method achieves joint model selection and model parameters estimation froman indirect observation of a textured image. Finally, the third method addresses the problemof joint deconvolution and segmentation of an image composed of several texturedregions, while estimating at the same time the parameters of each constituent texture.Last, but not least, the algorithmic contribution is represented by the development ofa new efficient version of the Metropolis Hastings algorithm, with a directional componentof the proposal function based on the”Newton direction” and the Fisher informationmatrix. This particular directional component allows for an efficient exploration of theparameter space and, consequently, increases the convergence speed of the algorithm.To summarize, this work presents a series of methods to solve three image processingproblems in the context of blurry and noisy textured images. Moreover, we present twoconnected contributions, one regarding the texture models andone meant to enhance theperformances of the samplers employed for all of the three methods.

Univ., Diss.--St. Gallen, 2006.

Zugl.: Köln, University, Diss., 2009.