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In longitudinal studies, data collected within a subject or cluster are somewhat correlated by their very nature and special cares are needed to account for such correlation in the analysis of data. Under the framework of longitudinal studies, three topics are being discussed in this thesis. In chapter 2, the joint modelling of multivariate longitudinal process consisting of different types of outcomes are discussed. In the large cohort study of UK north Stafforshire osteoarthritis project, longitudinal trivariate outcomes of continuous, binary and ordinary data are observed at baseline, year 3 and year 6. Instead of analysing each process separately, joint modelling is proposed for the trivariate outcomes to account for the inherent association by introducing random effects and the covariance matrix G. The influence of covariance matrix G on statistical inference of fixed-effects parameters has been investigated within the Bayesian framework. The study shows that by joint modelling the multivariate longitudinal process, it can reduce the bias and provide with more reliable results than it does by modelling each process separately. Together with the longitudinal measurements taken intermittently, a counting process of events in time is often being observed as well during a longitudinal study. It is of interest to investigate the relationship between time to event and longitudinal process, on the other hand, measurements taken for the longitudinal process may be potentially truncated by the terminated events, such as death. Thus, it may be crucial to jointly model the survival and longitudinal data. It is popular to propose linear mixed-effects models for the longitudinal process of continuous outcomes and Cox regression model for survival data to characterize the relationship between time to event and longitudinal process, and some standard assumptions have been made. In chapter 3, we try to investigate the influence on statistical inference for survival data when the assumption of mutual independence on random error of linear mixed-effects models of longitudinal process has been violated. And the study is conducted by utilising conditional score estimation approach, which provides with robust estimators and shares computational advantage. Generalised sufficient statistic of random effects is proposed to account for the correlation remaining among the random error, which is characterized by the data-driven method of modified Cholesky decomposition. The simulation study shows that, by doing so, it can provide with nearly unbiased estimation and efficient statistical inference as well. In chapter 4, it is trying to account for both the current and past information of longitudinal process into the survival models of joint modelling. In the last 15 to 20 years, it has been popular or even standard to assume that longitudinal process affects the counting process of events in time only through the current value, which, however, is not necessary to be true all the time, as recognised by the investigators in more recent studies. An integral over the trajectory of longitudinal process, along with a weighted curve, is proposed to account for both the current and past information to improve inference and reduce the under estimation of effects of longitudinal process on the risk hazards. A plausible approach of statistical inference for the proposed models has been proposed in the chapter, along with real data analysis and simulation study.

Cette thèse comporte trois chapitres dans lesquels j'étudie les coûts de transaction des actions, les anomalies en finance et les activités du système bancaire parallèle. Dans le premier chapitre (co-écrit avec René Garcia), une nouvelle façon d'estimer les coûts de transaction des actions est proposée. Les coûts de transaction ont diminué au fil du temps, mais ils peuvent augmenter considérablement lorsque la liquidité de financement se raréfi e, lorsque les craintes des investisseurs augmentent ou lorsqu'il y a d'autres frictions qui empêchent l'arbitrage. Nous estimons dans ce chapitre les écarts entre les cours acheteur et vendeur des actions de milliers d'entreprises à une fréquence journalière et présentons ces mouvements importants pour plusieurs de ces épisodes au cours des 30 dernières années. Le coût de transaction des trois quarts des actions est fortement impacté par la liquidité de fi nancement et augmente en moyenne de 24%. Alors que les actions des petites entreprises et celles des entreprises à forte volatilité ont des coûts de transaction plus élevés, l'augmentation relative des coûts de transaction en temps de crise est plus prononcée pour les actions des grandes entreprises et celles des entreprises à faible volatilité. L'écart entre les coûts de transaction respectifs de ces groupes de qualité élevée et qualité faible augmente également lorsque les conditions financières se détériorent, ce qui prouve le phénomène de fuite vers la qualité. Nous avons construit des portefeuilles basés sur des anomalies et avons estimé leurs "alphas" ajustés pour les coûts de rééquilibrage sur la base de nos estimations des coûts de transaction pour montrer que toutes les stratégies sont soit non rentables soit perdent de l'argent, à l'exception de deux anomalies: le "prix de l'action" et la "dynamique du secteur industriel". Dans le deuxième chapitre, j'étudie comment la popularité des anomalies dans les revues scienti ques spécialisées en finance peut influer sur le rendement des stratégies basées sur ces anomalies. J'utilise le ton du résumé de la publication dans laquelle une anomalie est discutée et le facteur d'impact de la revue dans laquelle cette publication a paru pour prévoir le rendement des stratégies basées sur ces anomalies sur la période après publication. La principale conclusion est la suivante: lorsqu'une anomalie est discutée dans une publication dont le résumé a un ton positif, et qui apparaît dans une revue avec un facteur d'impact supérieur à 3 (Journal of Finance, Journal of Financial Economics, Review of Financial Studies), cette anomalie est plus susceptible d'attirer les investisseurs qui vont baser leurs stratégies sur cette anomalie et corriger ainsi la mauvaise évaluation des actions. Le troisième chapitre (co-écrit avec Vasia Panousi) propose une mesure de l'activité bancaire parallèle des entreprises opérant dans le secteur financier aux États-Unis. À cette fi n, nous utilisons l'analyse de données textuelles en extrayant des informations des rapports annuels et trimestriels des entreprises. On constate que l'activité bancaire parallèle était plus élevée pour les "Institutions de dépôt", les "Institutions qui ne prennent pas de dépôt" et le secteur "Immobilier" avant 2008. Mais après 2008, l'activité bancaire parallèle a considérablement baissé pour toutes les fi rmes opérant dans le secteur financier sauf les "Institutions non dépositaires". Notre indice du système bancaire parallèle satisfait certains faits économiques concernant le système bancaire parallèle, en particulier le fait que les politiques monétaires restrictives contribuent à l'expansion du système bancaire parallèle. Nous montrons également avec notre indice que, lorsque l'activité bancaire parallèle des 100 plus grandes banques augmente, les taux de délinquance sur les prêts accordés par ces banques augmentent également. L'inverse est observé avec l'indice bancaire traditionnel: une augmentation de l'activité bancaire traditionnelle des 100 plus grandes banques diminue le taux de délinquance. / This thesis has three chapters in which I study transaction costs, anomalies and shadow banking activities. In the first chapter (co-authored with René Garcia) a novel way of estimating transaction costs is proposed. Transaction costs have declined over time but they can increase considerably when funding liquidity becomes scarce, investors' fears spike or other frictions limit arbitrage. We estimate bid-ask spreads of thousands of firms at a daily frequency and put forward these large movements for several of these episodes in the last 30 years. The transaction cost of three-quarters of the firms is significantly impacted by funding liquidity and increases on average by 24%. While small firms and high volatility firms have larger transaction costs, the relative increase in transaction costs in crisis times is more pronounced in large firms and low-volatility firms. The gap between the respective transaction costs of these high- and low-quality groups also increases when financial conditions deteriorate, which provides evidence of flight to quality. We build anomaly-based long-short portfolios and estimate their alphas adjusted for rebalancing costs based on our security-level transaction cost estimates to show that all strategies are either unprofitable or lose money, except for price per share and industry momentum. In the second chapter I study how the popularity of anomalies in peer-reviewed finance journals can influence the returns on these anomalies. I use the tone of the abstract of the publication in which an anomaly is discussed and the impact factor of the journal in which this publication appears to forecast the post-publication return of strategies based on the anomaly. The main finding is the following: when an anomaly is discussed in a positive tone publication that appears in a journal with an impact factor higher than 3 (Journal of Finance, Journal of Financial Economics, Review of Financial Studies), this anomaly is more likely to attract investors that are going to arbitrage away the mispricing. The third chapter (co-authored with Vasia Panousi) proposes a measure of the shadow banking activity of firms operating in the financial industry in the United States. For this purpose we use textual data analysis by extracting information from annual and quarterly reports of firms. We find that the shadow banking activity was higher for the “Depository Institutions", “Non depository Institutions" and the “Real estate" before 2008. But after 2008, the shadow banking activity dropped considerably for all the financial companies except for the “Non depository Institutions". Our shadow banking index satisfies some economic facts about the shadow banking, especially the fact that contractionary monetary policies contribute to expand shadow banking. We also show with our index that, when the shadow banking activity of the 100 biggest banks increases, the delinquency rates on the loans that these banks give also increases. The opposite is observed with the traditional banking index: an increase of the traditional banking activity of the 100 biggest banks decreases the delinquency rate.

This master's thesis deals with demonstration of various approaches to probabilistic inference in Bayesian networks. Basics of probability theory, introduction to Bayesian networks, methods for Bayesian inference and applications of Bayesian networks are described in theoretical part. Inference techniques are explained and complemented by their algorithm. Techniques are also illustrated on example. Practical part contains implementation description, experiments with demonstration applications and conclusion of the results.

當母體中有部份對象因被治癒或免疫而不會失敗時，需考慮這群對象所佔的比率，即存活分率。本文主要在探討如何以貝氏方法對含存活分率之治癒率模式進行分析，並特別針對兩種含存活分率的迴歸模式，分別是Weibull迴歸模式以及對數邏輯斯迴歸模式，導出概似函數與各參數之完全條件後驗分配及其性質。由於聯合後驗分配相當複雜，各參數之邊際後驗分配之解析形式很難表達出。所以，我們採用了馬可夫鏈蒙地卡羅方法（MCMC）中的Gibbs抽樣法及Metropolis法，模擬產生參數值，以進行貝氏分析。實證部份，我們分析了黑色素皮膚癌的資料，這是由美國Eastern Cooperative Oncology Group所進行的第三階段臨床試驗研究。有關模式選取的部份，我們先分別求出各對象在每個模式之下的條件預測指標（CPO），再據以算出各模式的對數擬邊際概似函數值（LPML），以比較各模式之適合性。 / When we face the problem that part of subjects have been cured or are immune so they never fail, we need to consider the fraction of this group among the whole population, which is the so called survival fraction. This article discuss that how to analyze cure rate models containing survival fraction based on Bayesian method. Two cure rate models containing survival fraction are focused; one is based on the Weibull regression model and the other is based on the log-logistic regression model. Then, we derive likelihood functions and full conditional posterior distributions under these two models. Since joint posterior distributions are both complicated, and marginal posterior distributions don’t have closed form, we take Gibbs sampling and Metropolis sampling of Markov Monte Carlo chain method to simulate parameter values. We illustrate how to conduct Bayesian analysis by using the data from a melanoma clinical trial in the third stage conducted by Eastern Cooperative Oncology Group. To do model selection, we compute the conditional predictive ordinate (CPO) for every subject under each model, then the goodness is determined by the comparing the value of log of pseudomarginal likelihood (LPML) of each model.