本研究以貝氏網路作為表示教學領域中各個學習觀念的關係的語言。教學領域中的學習觀念包含了基本觀念與綜合觀念，綜合觀念是由兩個以上的基本觀念所衍生出來的觀念，而綜合觀念的學習歷程即為學生在學習的過程中如何整合這些基本觀念的過程。了解綜合觀念的學習歷程可以幫助教師及出題者了解學生的學習路徑，並修改其教學或出題的方針，以期能提供適性化的教學及測驗。為了從考生答題資料中尋找出這個隱藏的綜合觀念學習歷程，我們提出一套以mutual information以及一套以chi-square test所發展出來的研究方法，希望能夠藉由一個模擬環境中模擬考生的答題資料來猜測考生學習綜合觀念的學習歷程。 初步的實驗結果顯示出，在一些特殊的條件假設下，我們的方法有不錯的機會找到暗藏在模擬系統中的學習歷程。因此我們進而嘗試提出一個策略來尋找較大規模結構中的學習歷程，利用搜尋的概念嘗試是否能較有效率的尋找出學生對於綜合觀念學習歷程。雖然在實驗中並沒有十分理想的結果，但是在實驗的過程中，我們除了發現學生答題資料的模糊程度為系統的正確率的主要挑戰之外，另外也發現了學生類別與觀念能力之間的關係也是影響實驗結果的主要因素。透過我們的方法，雖然不能完美的找出學生對於任何綜合觀念的綜合歷程，但是我們的實驗過程與結果也對隱藏的真實歷程結構提供了不少線索。 最後，我們探討如何藉由觀察學生接受測驗的結果來分類不同學習程度與狀況的學生之相關問題與技術。我們利用最近鄰居分類法與k-means分群法以及基於這些方法所變化出的方法，探討是否能透過學生的答題資料有效的分辨學生能力的類別。實驗結果顯示出，在每個觀念擁有多道測驗試題的情況下，利用最近鄰居分類法與k-means分群法以及基於這些方法所變化出的方法，藉由考生答題資料來進行學生能力類別的分類可以得到不錯的正確率。我們希望這些探討和結果能對適性化教學作出一些貢獻。 / In this thesis, I employ Bayesian networks to represent relations between concepts in pedagogical domains. We consider basic concepts, and composite concepts that are integrated from the basic ones. The learning processes of composite concepts are the ways how students integrate the basic concepts to form the composite concepts. Information about the learning processes can help teachers know the learning paths of students and revise their teaching methods so that teachers can provide adaptive course contents and assessments. In order to find out the latent learning processes based on students’ item response patterns, I propose two methods: a mutual information-based approach and a chi-square test-stimulated heuristics, and examine the ideas in a simulated environment. Results of some preliminary experiments showed that the proposed methods offered satisfactory performance under some particular conditions. Hence, I went a step further to propose a search method that tried to find out the learning process of larger structures in a more efficient way. Although the experimental results for the search method were not very satisfactory, we would find that both the uncertainty included by the students’ item response patterns and the relations between student groups and concepts substantially influenced the performance achieved by the proposed methods. Although the proposed methods did not find out the learning processes perfectly, the experimental processes and results indeed had the potential to provide information about the latent learning processes. Finally, I attempted to classify students’ competence according to their item response patterns. I used the nearest neighbor algorithm, the k-means algorithm, and some variations of these two algorithms to classify students’ competence patterns. Experimental results showed that the more the test items used in the assessment, the higher the accuracy of classification we could obtain. I hope that these experimental results can make contributions towards adaptive learning.

In this thesis we develop several kinds of latent variable models in order to address three types of bio-statistical problem. The three problems are the treatment effect of carcinogens on tumour development, spatial interactions between plant species and motor unit number estimation (MUNE). The three types of data looked at are: highly heterogeneous longitudinal count data, quadrat counts of species on a rectangular lattice and lastly, electrophysiological data consisting of measurements of compound muscle action potential (CMAP) area and amplitude. Chapter 1 sets out the structure and the development of ideas presented in this thesis from the point of view of: model structure, model selection, and efficiency of estimation. Chapter 2 is an introduction to the relevant literature that has in influenced the development of this thesis. In Chapter 3 we use the EM algorithm for an application of an autoregressive hidden Markov model to describe longitudinal counts. The data is collected from experiments to test the effect of carcinogens on tumour growth in mice. Here we develop forward and backward recursions for calculating the likelihood and for estimation. Chapter 4 is the analysis of a similar kind of data using a more sophisticated model, incorporating random effects, but estimation this time is conducted from the Bayesian perspective. Bayesian model selection is also explored. In Chapter 5 we move to the two dimensional lattice and construct a model for describing the spatial interaction of tree types. We also compare the merits of directed and undirected graphical models for describing the hidden lattice. Chapter 6 is the application of a Bayesian hierarchical model (MUNE), where the latent variable this time is multivariate Gaussian and dependent on a covariate, the stimulus. Model selection is carried out using the Bayes Information Criterion (BIC). In Chapter 7 we approach the same problem by using the reversible jump methodology (Green, 1995) where this time we use a dual Gaussian-Binary representation of the latent data. We conclude in Chapter 8 with suggestions for the direction of new work. In this thesis, all of the estimation carried out on real data has only been performed once we have been satisfied that estimation is able to retrieve the parameters from simulated data. Keywords: Amyotrophic lateral sclerosis (ALS), carcinogens, hidden Markov models (HMM), latent variable models, longitudinal data analysis, motor unit disease (MND), partially ordered Markov models (POMMs), the pseudo auto- logistic model, reversible jump, spatial interactions.

Working memory training improves performance on trained and untrained working memory tasks, but there is little consistent evidence that these gains benefit everyday tasks that rely on working memory. Evidence has shown that transcranial electrical stimulation (tES) may be an effective tool for enhancing cognitive training and promoting transfer. In the first study, participants completed Cogmed working memory training with either active or sham transcranial random noise stimulation (tRNS). Training was associated with substantial gains on the training activities and on transfer measures of working memory with common processing and storage demands to the training tasks. tRNS did not enhance gains on trained or untrained activities. The second study systematically investigated the boundary conditions to training transfer by testing whether gains following backward digit recall (BDR) training transferred within- and across-paradigm to untrained backward recall and n-back tasks with varying degrees of overlap with the training activity. A further aim was to test whether transcranial direct current stimulation (tDCS) enhanced training and transfer. Participants were allocated to one of three conditions: (i) BDR training with active tDCS, (ii) BDR training with sham tDCS, or (iii) visual search control training with sham tDCS. The results indicated that training transfer is constrained by paradigm, but not by stimuli domain or stimuli materials. There was no evidence that tDCS enhanced performance on the training or transfer tasks. The results of Study 1 and Study 2 provide no evidence that tES enhances the benefits of working memory training. The absence of transfer between backward recall training and n-back in Study 2 suggested the tasks might tap into distinct aspects of working memory. Consequently, the final study used a latent variable approach to explore the degree of overlap between different forms of backward recall and n-back tasks containing digits, letters, or spatial locations as stimuli. The best-fitting factor model included two distinct but related (r = .68) constructs corresponding to backward recall and n-back. Both categories of task were linked to a separate fluid reasoning construct, providing evidence that both are valid measures of higher-order complex cognition. Overall, the experiments in this thesis suggest that working memory tasks tap into separate processes and that training may be targeting and improving these distinct processes, explaining the absence of cross-paradigm transfer.

Made available in DSpace on 2009-11-18T19:01:13Z (GMT). No. of bitstreams: 0 Previous issue date: 2004 / A Física e a Administração concentram suas pesquisas sobre fenômenos que, de certa forma, se assemelham, fazendo com que nos questionemos a respeito da grande integral do universo a que estamos submetidos. Em uma exploração por analogias, aproxima-se aqui o mundo organizacional ao dos sistemas UnIVerSaIS, instáveis e não-integráveis, onde a flecha do tempo é quem determina a evolução dos mesmos. Mostra-se que na Administração, como na Física, tudo parece convergir na direção de um inesgotável repertório de bifurcações e possibilidades para o destino mercadológico de produtos, serviços e marcas ao longo de um continuum. Para amenizar os efeitos dessas incertezas, é buscada uma simplificação desses complexos sistemas sociais através de uma proposta de modelo baseado em fatores consagrados pela literatura da gestão empresarial como norteadores das escolhas dos consumidores; um processo gaussiano da 'percepção do valor', que pode servir de ferramenta nas decisões estratégicas e gerenciais dentro das empresas. / The physical and the administration sciences focus their researches on phenomenum wich, in some ways, can have similarities, making us to question and ask about the great convergence ofthe systems in the Universe under which we are submitted. Exploring by analogues, this research tries to make sense to put together the organizational and physical systems, unstables and not integratable, moving forward by the time's arrow, that determines the evolution ofthose. In the Administration, as in the Physics, everything seems to converge at the direction of an inexhaustible collection of forks and possibilities, if considering the destiny of products, services and labels during the human history. To soften the effects of those uncertanties, it is fetched a simplification of these complex social systems across a proposal of a model to be constructed and tested, based in some factors established by business management's literature as the guiders of the consumers's choices; a gaussian process of the 'insight value', that can be useful as a tool for the strategic and business managing decisions beyond the companies.

Over the past two decades there has been an upsurge in interest in structural equation modelling (SEM). Applications abound in the social sciences and econometrics, but the use of this multivariate technique is not so common in public health research. This dissertation discusses the methodology, the criticisms and practical problems of SEM. We examine actual applications of SEM in public health research. Comparisons are made between multiple regression and SEM and between factor analysis and SEM. A complex model investigating the utilization of antenatal care services (ANC) by migrant women in Belgium is analysed using SEM. The dissertation concludes with a discussion of the results found and on the use of SEM in public health research. Structural equation modelling is recommended as a tool for public health researchers with a warning against using the technique too casually. / Mathematical Sciences / M. Sc. (Statistics)

Language is the principal medium for ideas, while dialogue is the most natural and effective way for humans to interact with and access information from machines. Natural language generation (NLG) is a critical component of spoken dialogue and it has a significant impact on usability and perceived quality. Many commonly used NLG systems employ rules and heuristics, which tend to generate inflexible and stylised responses without the natural variation of human language. However, the frequent repetition of identical output forms can quickly make dialogue become tedious for most real-world users. Additionally, these rules and heuristics are not scalable and hence not trivially extensible to other domains or languages. A statistical approach to language generation can learn language decisions directly from data without relying on hand-coded rules or heuristics, which brings scalability and flexibility to NLG. Statistical models also provide an opportunity to learn in-domain human colloquialisms and cross-domain model adaptations. A robust and quasi-supervised NLG model is proposed in this thesis. The model leverages a Recurrent Neural Network (RNN)-based surface realiser and a gating mechanism applied to input semantics. The model is motivated by the Long-Short Term Memory (LSTM) network. The RNN-based surface realiser and gating mechanism use a neural network to learn end-to-end language generation decisions from input dialogue act and sentence pairs; it also integrates sentence planning and surface realisation into a single optimisation problem. The single optimisation not only bypasses the costly intermediate linguistic annotations but also generates more natural and human-like responses. Furthermore, a domain adaptation study shows that the proposed model can be readily adapted and extended to new dialogue domains via a proposed recipe. Continuing the success of end-to-end learning, the second part of the thesis speculates on building an end-to-end dialogue system by framing it as a conditional generation problem. The proposed model encapsulates a belief tracker with a minimal state representation and a generator that takes the dialogue context to produce responses. These features suggest comprehension and fast learning. The proposed model is capable of understanding requests and accomplishing tasks after training on only a few hundred human-human dialogues. A complementary Wizard-of-Oz data collection method is also introduced to facilitate the collection of human-human conversations from online workers. The results demonstrate that the proposed model can talk to human judges naturally, without any difficulty, for a sample application domain. In addition, the results also suggest that the introduction of a stochastic latent variable can help the system model intrinsic variation in communicative intention much better.

La plupart des systèmes de recommandation actuels se base sur des évaluations sous forme de notes (i.e., chiffre entre 0 et 5) pour conseiller un contenu (film, restaurant...) à un utilisateur. Ce dernier a souvent la possibilité de commenter ce contenu sous forme de texte en plus de l'évaluer. Il est difficile d'extraire de l'information d'un texte brut tandis qu'une simple note contient peu d'information sur le contenu et l'utilisateur. Dans cette thèse, nous tentons de suggérer à l'utilisateur un texte lisible personnalisé pour l'aider à se faire rapidement une opinion à propos d'un contenu. Plus spécifiquement, nous construisons d'abord un modèle thématique prédisant une description de film personnalisée à partir de commentaires textuels. Notre modèle sépare les thèmes qualitatifs (i.e., véhiculant une opinion) des thèmes descriptifs en combinant des commentaires textuels et des notes sous forme de nombres dans un modèle probabiliste joint. Nous évaluons notre modèle sur une base de données IMDB et illustrons ses performances à travers la comparaison de thèmes. Nous étudions ensuite l'inférence de paramètres dans des modèles à variables latentes à grande échelle, incluant la plupart des modèles thématiques. Nous proposons un traitement unifié de l'inférence en ligne pour les modèles à variables latentes à partir de familles exponentielles non-canoniques et faisons explicitement apparaître les liens existants entre plusieurs méthodes fréquentistes et Bayesiennes proposées auparavant. Nous proposons aussi une nouvelle méthode d'inférence pour l'estimation fréquentiste des paramètres qui adapte les méthodes MCMC à l'inférence en ligne des modèles à variables latentes en utilisant proprement un échantillonnage de Gibbs local. Pour le modèle thématique d'allocation de Dirichlet latente, nous fournissons une vaste série d'expériences et de comparaisons avec des travaux existants dans laquelle notre nouvelle approche est plus performante que les méthodes proposées auparavant. Enfin, nous proposons une nouvelle classe de processus ponctuels déterminantaux (PPD) qui peut être manipulée pour l'inférence et l'apprentissage de paramètres en un temps potentiellement sous-linéaire en le nombre d'objets. Cette classe, basée sur une factorisation spécifique de faible rang du noyau marginal, est particulièrement adaptée à une sous-classe de PPD continus et de PPD définis sur un nombre exponentiel d'objets. Nous appliquons cette classe à la modélisation de documents textuels comme échantillons d'un PPD sur les phrases et proposons une formulation du maximum de vraisemblance conditionnel pour modéliser les proportions de thèmes, ce qui est rendu possible sans aucune approximation avec notre classe de PPD. Nous présentons une application à la synthèse de documents avec un PPD sur 2 à la puissance 500 objets, où les résumés sont composés de phrases lisibles. / Most of current recommendation systems are based on ratings (i.e. numbers between 0 and 5) and try to suggest a content (movie, restaurant...) to a user. These systems usually allow users to provide a text review for this content in addition to ratings. It is hard to extract useful information from raw text while a rating does not contain much information on the content and the user. In this thesis, we tackle the problem of suggesting personalized readable text to users to help them make a quick decision about a content. More specifically, we first build a topic model that predicts personalized movie description from text reviews. Our model extracts distinct qualitative (i.e., which convey opinion) and descriptive topics by combining text reviews and movie ratings in a joint probabilistic model. We evaluate our model on an IMDB dataset and illustrate its performance through comparison of topics. We then study parameter inference in large-scale latent variable models, that include most topic models. We propose a unified treatment of online inference for latent variable models from a non-canonical exponential family, and draw explicit links between several previously proposed frequentist or Bayesian methods. We also propose a novel inference method for the frequentist estimation of parameters, that adapts MCMC methods to online inference of latent variable models with the proper use of local Gibbs sampling.~For the specific latent Dirichlet allocation topic model, we provide an extensive set of experiments and comparisons with existing work, where our new approach outperforms all previously proposed methods. Finally, we propose a new class of determinantal point processes (DPPs) which can be manipulated for inference and parameter learning in potentially sublinear time in the number of items. This class, based on a specific low-rank factorization of the marginal kernel, is particularly suited to a subclass of continuous DPPs and DPPs defined on exponentially many items. We apply this new class to modelling text documents as sampling a DPP of sentences, and propose a conditional maximum likelihood formulation to model topic proportions, which is made possible with no approximation for our class of DPPs. We present an application to document summarization with a DPP on 2 to the power 500 items, where the summaries are composed of readable sentences.

This thesis considers the problem of assigning a sentence its syntactic structure, which may be discontinuous. It proposes a class of models based on probabilistic grammars that are obtained by the automatic refinement of a given grammar. Different strategies for parsing with a refined grammar are developed. The induction, refinement, and application of two types of grammars (linear context-free rewriting systems and hybrid grammars) are evaluated empirically on two German and one Dutch corpus.

Fast detection and identification of unknown substances is an area of interest for many parties. Raman spectroscopy is a laser-based method allowing for long range no contact investigation of substances. A Coded Aperture Snapshot Spectral Imaging (CASSI) system allows for fast and efficient measurements of hyperspectral images of a scene, containing a mixture of the spatial and spectral data. To analyze the scene and the unknown substances within it, it is required that the spectra in each spatial position are known. Utilizing the theory of compressed sensing allows for reconstruction of hyperspectral images of a scene given their CASSI measurements by assuming a sparsity prior. These reconstructions can then be utilized by a human operator to deduce and classify the unknown substances and their spatial locations in the scene. Such classifications are then applicable as decision support in various areas, for example in the judicial system. Reconstruction of hyperspectral images given CASSI-measurements is an ill-posed inverse problem typically solved by utilizing regularization techniques such as total variation (TV). These TV-based reconstruction methods are time consuming relative to the time needed to acquire the CASSI measurements, which is in the order of seconds. This leads to a reduced number of areas where the technology is applicable. In this thesis, a Generative Adversarial Network (GAN) based reconstruction method is proposed. A GAN is trained using simulated training data consisting of hyperspectral images and their respective CASSI measurements. The GAN provides a learned prior, and is used in an iterative optimization algorithm seeking to find an optimal set of latent variables such that the reconstruction error is minimized. The results of the developed GAN based reconstruction method are compared with a traditional TV method and a different machine learning based reconstruction method.  The results show that the reconstruction method developed in this thesis performs better than the compared methods in terms of reconstruction quality in short time spans.

Cette thèse est organisée en trois chapitres où sont développées des méthodes de simulation à posteriori pour inférence Bayesienne dans des modèles espace-état ainsi que des modèles économétriques pour l’analyse de données financières. Au chapitre 1, nous considérons le problème de simulation a posteriori dans les modèles espace-état univariés et non-Gaussiens. Nous proposons une nouvelle méthode de Monte-Carlo par chaînes de Markov (MCMC) mettant à jour le vecteur de paramètres de la dynamique d’état ainsi que la séquence de variables d’état conjointement dans un bloc unique. La proposition MCMC est tirée en deux étapes: la distribution marginale du vecteur de paramètres de la dynamique d’état est construite en utilisant une approximation du gradient et du Hessien du logarithme de sa densité a posteriori, pour laquelle le vecteur de variables d’état a été intégré. La distribution conditionnelle de la séquence de variables d’état, étant donné la proposition du vecteur de paramètres, est telle que décrite dans McCausland (2012). Le calcul du gradient et du Hessien approximatif combine des sous-produits de calcul du tirage d’état avec une quantité modeste de calculs supplémentaires. Nous comparons l’efficacité numérique de notre simulation a posteriori à celle de la méthode Ancillarity-Sufficiency Interweaving Strategy (ASIS) décrite dans Kastner & Frühwirth-Schnatter (2014), en utilisant un modèle de volatilité stochastique Gaussien et le même panel de 23 taux de change quotidiens utilisé dans ce même article. Pour calculer la moyenne a posteriori du paramètre de persistance de la volatilité, notre efficacité numérique est de 6 à 27 fois plus élevée; pour la volatilité du paramètre de volatilité, elle est de 18 à 53 fois plus élevée. Nous analysons dans un second exemple des données de compte de transaction avec un modèle Poisson et Gamma-Poisson dynamique. Malgré la nature non Gaussienne des données de compte, nous obtenons une efficacité numérique élevée, guère inférieure à celle rapportée dans McCausland (2012) pour une méthode d’échantillonnage impliquant un calcul préliminaire de la forme de la distribution a posteriori statique des paramètres. Au chapitre 2, nous proposons un nouveau modèle de durée conditionnelle stochastique (SCD) pour l’analyse de données de transactions financières en haute fréquence. Nous identifions certaines caractéristiques indésirables des densités de durée conditionnelles paramétriques existantes et proposons une nouvelle famille de densités conditionnelles flexibles pouvant correspondre à une grande variété de distributions avec des fonctions de taux de probabilité modérément variable. Guidés par des considérations théoriques issues de la théorie des files d’attente, nous introduisons des déviations non-paramétriques autour d’une distribution exponentielle centrale, qui, selon nous, est un bon modèle de premier ordre pour les durées financières, en utilisant une densité de Bernstein. La densité résultante est non seulement flexible, dans le sens qu’elle peut s’approcher de n’importe quelle densité continue sur [0, ∞) de manière arbitraire, à condition qu’elle se compose d’un nombre suffisamment grand de termes, mais également susceptible de rétrécissement vers la distribution exponentielle. Grâce aux tirages très efficaces des variables d’état, l’efficacité numérique de notre simulation a posteriori se compare très favorablement à celles obtenues dans les études précédentes. Nous illustrons nos méthodes à l’aide des données de cotation d’actions négociées à la Bourse de Toronto. Nous constatons que les modèles utilisant notre densité conditionnelle avec moins de qua- tre termes offrent le meilleur ajustement. La variation régulière trouvée dans les fonctions de taux de probabilité, ainsi que la possibilité qu’elle ne soit pas monotone, aurait été impossible à saisir avec une spécification paramétrique couramment utilisée. Au chapitre 3, nous présentons un nouveau modèle de durée stochastique pour les temps de transaction dans les marchés d’actifs. Nous soutenons que les règles largement acceptées pour l’agrégation de transactions apparemment liées induisent une inférence erronée concernant les durées entre des transactions non liées: alors que deux transactions exécutées au cours de la même seconde sont probablement liées, il est extrêmement improbable que toutes paires de transactions le soient, dans un échantillon typique. En plaçant une incertitude sur les transactions liées dans notre modèle, nous améliorons l’inférence pour la distribution de la durée entre les transactions non liées, en particulier près de zéro. Nous proposons un modèle en temps discret pour les temps de transaction censurés permettant des valeurs nulles excessives résultant des durées entre les transactions liées. La distribution discrète des durées entre les transactions indépendantes découle d’une densité flexible susceptible de rétrécissement vers une distribution exponentielle. Dans un exemple empirique, nous constatons que la fonction de taux de probabilité conditionnelle sous-jacente pour des durées (non censurées) entre transactions non liées varie beaucoup moins que celles trouvées dans la plupart des études; une distribution discrète pour les transactions non liées basée sur une distribution exponentielle fournit le meilleur ajustement pour les trois séries analysées. Nous prétendons que c’est parce que nous évitons les artefacts statistiques qui résultent de règles déterministes d’agrégation des échanges et d’une distribution paramétrique inadaptée. / This thesis is organized in three chapters which develop posterior simulation methods for Bayesian inference in state space models and econometrics models for the analysis of financial data. In Chapter 1, we consider the problem of posterior simulation in state space models with non-linear non-Gaussian observables and univariate Gaussian states. We propose a new Markov Chain Monte Carlo (MCMC) method that updates the parameter vector of the state dynamics and the state sequence together as a single block. The MCMC proposal is drawn in two steps: the marginal proposal distribution for the parameter vector is constructed using an approximation of the gradient and Hessian of its log posterior density, with the state vector integrated out. The conditional proposal distribution for the state sequence given the proposal of the parameter vector is the one described in McCausland (2012). Computation of the approximate gradient and Hessian combines computational by-products of the state draw with a modest amount of additional computation. We compare the numerical efficiency of our posterior simulation with that of the Ancillarity-Sufficiency Interweaving Strategy (ASIS) described in Kastner & Frühwirth-Schnatter (2014), using the Gaus- sian stochastic volatility model and the panel of 23 daily exchange rates from that paper. For computing the posterior mean of the volatility persistence parameter, our numerical efficiency is 6-27 times higher; for the volatility of volatility parameter, 18-53 times higher. We analyse trans- action counts in a second example using dynamic Poisson and Gamma-Poisson models. Despite non-Gaussianity of the count data, we obtain high numerical efficiency that is not much lower than that reported in McCausland (2012) for a sampler that involves pre-computing the shape of a static posterior distribution of parameters. In Chapter 2, we propose a new stochastic conditional duration model (SCD) for the analysis of high-frequency financial transaction data. We identify undesirable features of existing parametric conditional duration densities and propose a new family of flexible conditional densities capable of matching a wide variety of distributions with moderately varying hazard functions. Guided by theoretical consideration from queuing theory, we introduce nonparametric deviations around a central exponential distribution, which we argue is a sound first-order model for financial durations, using a Bernstein density. The resulting density is not only flexible, in the sense that it can approximate any continuous density on [0,∞) arbitrarily closely, provided it consists of a large enough number of terms, but also amenable to shrinkage towards the exponential distribution. Thank to highly efficiency draws of state variables, numerical efficiency of our posterior simulation compares very favourably with those obtained in previous studies. We illustrate our methods using quotation data on equities traded on the Toronto Stock Exchange. We find that models with our proposed conditional density having less than four terms provide the best fit. The smooth variation found in the hazard functions, together with the possibility of it being non-monotonic, would have been impossible to capture using commonly used parametric specification. In Chapter 3, we introduce a new stochastic duration model for transaction times in asset markets. We argue that widely accepted rules for aggregating seemingly related trades mislead inference pertaining to durations between unrelated trades: while any two trades executed in the same second are probably related, it is extremely unlikely that all such pairs of trades are, in a typical sample. By placing uncertainty about which trades are related within our model, we improve inference for the distribution of duration between unrelated trades, especially near zero. We propose a discrete model for censored transaction times allowing for zero-inflation resulting from clusters of related trades. The discrete distribution of durations between unrelated trades arises from a flexible density amenable to shrinkage towards an exponential distribution. In an empirical example, we find that the underlying conditional hazard function for (uncensored) durations between unrelated trades varies much less than what most studies find; a discrete distribution for unrelated trades based on an exponential distribution provides a better fit for all three series analyzed. We claim that this is because we avoid statistical artifacts that arise from deterministic trade-aggregation rules and unsuitable parametric distribution.