L’utilisation des mesures subjectives en épidémiologie s’est intensifiée récemment, notamment avec la volonté de plus en plus affirmée d’intégrer la perception qu’ont les sujets de leur santé dans l’étude des maladies et l’évaluation des interventions. La psychométrie regroupe les méthodes statistiques utilisées pour la construction des questionnaires et l’analyse des données qui en sont issues. Ce travail de thèse avait pour but d’explorer différents problèmes méthodologiques soulevés par l’utilisation des techniques psychométriques en épidémiologie. Trois études empiriques sont présentées et concernent 1/ la phase de validation de l’instrument : l’objectif était de développer, à l’aide de données simulées, un outil de calcul de la taille d’échantillon pour la validation d’échelle en psychiatrie ; 2/ les propriétés mathématiques de la mesure obtenue : l’objectif était de comparer les performances de la différence minimale cliniquement pertinente d’un questionnaire calculée sur des données de cohorte, soit dans le cadre de la théorie classique des tests (CTT), soit dans celui de la théorie de réponse à l’item (IRT) ; 3/ son utilisation dans un schéma longitudinal : l’objectif était de comparer, à l’aide de données simulées, les performances d’une méthode statistique d’analyse de l’évolution longitudinale d’un phénomène subjectif mesuré à l’aide de la CTT ou de l’IRT, en particulier lorsque certains items disponibles pour la mesure différaient à chaque temps. Enfin, l’utilisation de graphes orientés acycliques a permis de discuter, à l’aide des résultats de ces trois études, la notion de biais d’information lors de l’utilisation des mesures subjectives en épidémiologie. / Recently, subjective measurements have increasingly been used in epidemiology, alongside the growing will to integrate individuals’ point of view on their health in studies on diseases or health interventions. Psychometrics includes statistical methods used to develop questionnaires and to analyze questionnaire data. This doctoral dissertation aimed to explore methodological issues raised by the use of psychometric techniques in epidemiology. Three empirical studies are presented and cover 1 / the validation stage of a questionnaire: the objective was to develop, using simulated data, a tool to determine sample size for internal validity studies on psychiatric scale; 2 / the mathematical properties of the subjective measurement: the objective was to compare the performances of the minimal clinically important difference of a questionnaire, assessed on data from a cohort study, computed using the classical test theory (CTT) framework or the item response theory framework (IRT); 3 / its use in a longitudinal design: the objective was to compare, using simulated data, the performances of a statistical method aimed to analyze the longitudinal course of a subjective phenomenon measured using the CTT or IRT framework, especially when some of the available items used for its measurement differ at each time of data collection. Finally, directed acyclic graphs were used to discuss the results from these three studies and the concept of information bias when subjective measurements are used in epidemiology.

[pt] A habilidade de determinar o momento ótimo para investir proporciona uma vantagem estratégica para as empresas em um ambiente competitivo. Se por um lado as incertezas exógenas podem ser fontes inibidoras do investimento, sob pressão dos competidores, essas empresas podem auferir uma vantagem competitiva caso invistam primeiro. Esta tese sintetiza os conceitos aplicados às metodologias de Opções Reais e da Teoria dos Jogos para propor uma metodologia de avaliação que contribui para a análise financeira de investimentos no mercado imobiliário. O primeiro modelo da tese é um modelo econométrico que considera as inter-relações na formação dos preços que compõem a dinâmica do mercado imobiliário do Rio de Janeiro, através de um modelo de autorregressão vetorial (VAR) identificado por grafos acíclicos direcionados. O objetivo deste trabalho é o de determinar a estratégia ótima de exercício da opção de investimento no equilíbrio de Nash considerando a incerteza na demanda por imóveis em uma região do Rio de Janeiro. Para tanto, o segundo modelo da tese adota uma versão modificada da metodologia de Grenadier (2002) com uma especificação mais adequada e robusta das incertezas para a função de demanda estocástica, em que foi inserida uma elasticidade do fator estocástico. Os parâmetros do modelo foram estimados com ferramentas econométricas a partir de dados reais do mercado imobiliário carioca. Foram realizadas simulações de Monte Carlo da demanda de forma a comparar os oligopólios em termos de níveis de investimento e quantidade produzida. Os resultados obtidos nos modelos de Jogos de Opções Reais desenvolvidos são intuitivos no sentido de que quanto maior a quantidade de concorrentes, menor o nível de demanda (gatilho) exigido para o investimento em novas unidades e quanto maior a volatilidade da demanda, maior o nível de demanda para ser ótimo o investimento. / [en] The ability to determine the optimal investment timing provides a strategic advantage for companies working in a competitive environment. While on the one hand, exogenous uncertainties may inhibit investment, under pressure from competitors, these firms can gain a competitive advantage if they are first movers. This thesis summarizes the concepts applied to Real Options and Game Theory methodologies to propose an evaluation methodology that contributes to the financial analysis of investments in the real estate market. The first model of the thesis is an econometric model that considers the interrelationships in the formation of prices that compose the real estate market dynamics of Rio de Janeiro, through a vector autoregression (VAR) model identified by directed acyclic graphs. The objective of this work is to determine the optimal strategy to exercise the investment option in the Nash equilibrium considering the uncertainty in the real estate demand in a region of Rio de Janeiro. To this end, the second model of the thesis adopted a modified version of the Grenadier (2002) methodology with a more adequate and robust specification of the uncertainties for the stochastic demand function, in which a stochastic factor elasticity was inserted. The parameters of the model were estimated using econometric tools based on real data from the real estate market in Rio de Janeiro. Monte Carlo simulations of demand were performed to compare the oligopolies in terms of levels of investment and quantity produced. The quantitative results obtained are intuitive in the sense that the larger the number of competitors, the lower the level of demand (threshold) required for investment in new units, whereas the greater the volatility of demand, the greater the demand threshold for the investment to be optimal.

Sequence alignment is one of the most intensely studied problems in bioinformatics, and is an important step in a wide range of analyses. An issue that has gained much attention in recent years is the fact that downstream analyses are often highly sensitive to the specific choice of alignment. One way to address this is to jointly sample alignments along with other parameters of interest. In order to extend the range of applicability of this approach, the first chapter of this thesis introduces a probabilistic evolutionary model for protein structures on a phylogenetic tree; since protein structures typically diverge much more slowly than sequences, this allows for more reliable detection of remote homologies, improving the accuracy of the resulting alignments and trees, and reducing sensitivity of the results to the choice of dataset. In order to carry out inference under such a model, a number of new Markov chain Monte Carlo approaches are developed, allowing for more efficient convergence and mixing on the high-dimensional parameter space. The second part of the thesis presents a directed acyclic graph (DAG)-based approach for representing a collection of sampled alignments. This DAG representation allows the initial collection of samples to be used to generate a larger set of alignments under the same approximate distribution, enabling posterior alignment probabilities to be estimated reliably from a reasonable number of samples. If desired, summary alignments can then be generated as maximum-weight paths through the DAG, under various types of loss or scoring functions. The acyclic nature of the graph also permits various other types of algorithms to be easily adapted to operate on the entire set of alignments in the DAG. In the final part of this work, methodology is introduced for alignment-DAG-based sequence annotation using hidden Markov models, and RNA secondary structure prediction using stochastic context-free grammars. Results on test datasets indicate that the additional information contained within the DAG allows for improved predictions, resulting in substantial gains over simply analysing a set of alignments one by one.