The spread between interest rate and sovereign bond rate is commonly used in- dicator for country's probability to default. Existing literature proposes many different potential spread determinants but fails to agree on which of them are important. As a result, there is a considerable uncertainty about the cor- rect model explaining the spread. We address this uncertainty by employing Bayesian Model Averaging method (BMA). The BMA technique attempts to consider all the possible combinations of variables and averages them using a model fit measure as weights. For this empirical exercise, we consider 20 different explanatory variables for a panel of 47 countries for the 1980-2010 period. Most of the previously suggested determinants were attributed high inclusion probabilities. Only the "foreign exchange reserves growth" and the "exports growth" scored low by their inclusion probabilities. We also find a role of variables previously not included in the literature's spread determinants - "openness" and "unemployment" which rank high by the inclusion probability. These results are robust to a wide range of both parameter and model priors. JEL Classification C6, C8, C11, C51, E43 Keywords Sovereign Spread Determinants, Model Uncer- tainty, Bayesian Model Averaging Author's e-mail semanv()gmail()com...

Inflation is one of the often used monetary indicators in conducting monetary policy. Even though money supply is an essential determinant of inflation, it is not used in inflation modeling. Currently, output gap is considered as most predicative variable. This thesis brings the empirical evidence on the hypothesis of money supply carrying more information on estimating inflation than the output gap. It is provided on the case of 16 developed European economies using Bayesian Model Averaging (BMA). BMA is a comprehensive approach that deals with the model uncertainty and thus solves the variable selection problem. The results of analysis confirmed that money supply includes more information of inflation than the output gap and thus should be used in inflation modeling. These outcomes are robust towards prior selection and high correlation of some variables.

Data from the 1995 National Health Interview Survey (NHIS) indicate that, due to chronic conditions, the onset of activity limitation typically occurs between age 40-70 years (i.e., the proportion of young adults with activity limitation is small and roughly constant with age and then it starts to change, roughly increasing). We use a Bayesian hierarchical model to detect the change point of a positive activity limitation status (ALS) across twelve domains based on race, gender, and education. We have two types of data: weighted and unweighted. We obtain weighted binomial counts using a regression analysis with the sample weights. Given the proportion of individuals in the population with positive ALS, we assume that the number of individuals with positive ALS at each age group has a binomial probability mass function. The proportions across age are different, and have the same beta distribution up to the change point (unknown), and the proportions after the change point have a different beta distribution. We consider two different analyses. The first considers each domain individually in its own model and the second considers the twelve domains simultaneously in a single model to“borrow strength" as in small area estimation. It is reasonable to assume that each domain has its own onset.In the first analysis, we use the Gibbs sampler to fit the model, and a computation of the marginal likelihoods, using an output analysis from the Gibbs sampler, provides the posterior distribution of the change point. We note that a reversible jump sampler fails in this analysis because it tends to get stuck either age 40 or age 70. In the second analysis, we use the Gibbs sampler to fit only the joint posterior distribution of the twelve change points. This is a difficult problem because the joint density requires the numerical computation of a triple integral at each iteration. The other parameters of the process are obtained using data augmentation by a Metropolis sampler and a Rao-Blackwellization. We found that overall the age of onset is about 50 to 60 years.

In this paper, we examine the determinants of outward FDI from four major OECD investors, namely, the US, Germany, France, and the Netherlands, to 129 developing countries classified under five regions over the period 1995-2008. Our goal is to distinguish whether the motivation for FDI differs among these investors in developing countries. Rather than relying on specific theories of FDI determinants, we examine them all simultaneously by employing Bayesian model averaging (BMA). This approach permits us to select the most appropriate model (or combination of models) that governs FDI allocation and to distinguish robust FDI determinants. We find that no single theory governs the decision of OECD FDI in developing countries but a combination of theories. In particular, OECD investors search for destinations with whom they have established intensive trade relations and that offer a qualified labor force. Low wages and attractive tax rates are robust investment criteria too, and a considerable share of FDI is still resource-driven. Overall, investors show fairly similar strategies in the five developing regions.

Topic of mergers and acquisitions (M&A) is popular both in academia and financial circles and press. A great deal of research has been focused on the value creation side of M&A deals, nonetheless factors influencing the particular method of payment used in M&A transactions are equally interesting. This thesis focuses on number of factors influencing the choice of medium of exchange in M&A deals with European Union domiciled bidders. Using Bayesian model averaging and a relatively new dataset of transactions announced between 2010 and 2018, the analysis finds several bidder, target and deal specific characteristics to be of a provable effect on the choice of payment. Finally, several enhancements and research questions for a further research are identified.

This dissertation research consists of two topics, population stochastics approximation Monte Carlo (Pop-SAMC) for Baysian model selection problems and ChIP-chip data analysis. The following two paragraphs give a brief introduction to each of the two topics, respectively. Although the reversible jump MCMC (RJMCMC) has the ability to traverse the space of possible models in Bayesian model selection problems, it is prone to becoming trapped into local mode, when the model space is complex. SAMC, proposed by Liang, Liu and Carroll, essentially overcomes the difficulty in dimension-jumping moves, by introducing a self-adjusting mechanism. However, this learning mechanism has not yet reached its maximum efficiency. In this dissertation, we propose a Pop-SAMC algorithm; it works on population chains of SAMC, which can provide a more efficient self-adjusting mechanism and make use of crossover operator from genetic algorithms to further increase its efficiency. Under mild conditions, the convergence of this algorithm is proved. The effectiveness of Pop-SAMC in Bayesian model selection problems is examined through a change-point identification example and a large-p linear regression variable selection example. The numerical results indicate that Pop- SAMC outperforms both the single chain SAMC and RJMCMC significantly. In the ChIP-chip data analysis study, we developed two methodologies to identify the transcription factor binding sites: Bayesian latent model and population-based test. The former models the neighboring dependence of probes by introducing a latent indicator vector; The later provides a nonparametric method for evaluation of test scores in a multiple hypothesis test by making use of population information of samples. Both methods are applied to real and simulated datasets. The numerical results indicate the Bayesian latent model can outperform the existing methods, especially when the data contain outliers, and the use of population information can significantly improve the power of multiple hypothesis tests.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Cette thèse présente des méthodes de traitement de données de comptage en particulier et des données discrètes en général. Il s'inscrit dans le cadre d'un projet stratégique du CRNSG, nommé CC-Bio, dont l'objectif est d'évaluer l'impact des changements climatiques sur la répartition des espèces animales et végétales. Après une brève introduction aux notions de biogéographie et aux modèles linéaires mixtes généralisés aux chapitres 1 et 2 respectivement, ma thèse s'articulera autour de trois idées majeures. Premièrement, nous introduisons au chapitre 3 une nouvelle forme de distribution dont les composantes ont pour distributions marginales des lois de Poisson ou des lois de Skellam. Cette nouvelle spécification permet d'incorporer de l'information pertinente sur la nature des corrélations entre toutes les composantes. De plus, nous présentons certaines propriétés de ladite distribution. Contrairement à la distribution multidimensionnelle de Poisson qu'elle généralise, celle-ci permet de traiter les variables avec des corrélations positives et/ou négatives. Une simulation permet d'illustrer les méthodes d'estimation dans le cas bidimensionnel. Les résultats obtenus par les méthodes bayésiennes par les chaînes de Markov par Monte Carlo (CMMC) indiquent un biais relatif assez faible de moins de 5% pour les coefficients de régression des moyennes contrairement à ceux du terme de covariance qui semblent un peu plus volatils. Deuxièmement, le chapitre 4 présente une extension de la régression multidimensionnelle de Poisson avec des effets aléatoires ayant une densité gamma. En effet, conscients du fait que les données d'abondance des espèces présentent une forte dispersion, ce qui rendrait fallacieux les estimateurs et écarts types obtenus, nous privilégions une approche basée sur l'intégration par Monte Carlo grâce à l'échantillonnage préférentiel. L'approche demeure la même qu'au chapitre précédent, c'est-à-dire que l'idée est de simuler des variables latentes indépendantes et de se retrouver dans le cadre d'un modèle linéaire mixte généralisé (GLMM) conventionnel avec des effets aléatoires de densité gamma. Même si l'hypothèse d'une connaissance a priori des paramètres de dispersion semble trop forte, une analyse de sensibilité basée sur la qualité de l'ajustement permet de démontrer la robustesse de notre méthode. Troisièmement, dans le dernier chapitre, nous nous intéressons à la définition et à la construction d'une mesure de concordance donc de corrélation pour les données augmentées en zéro par la modélisation de copules gaussiennes. Contrairement au tau de Kendall dont les valeurs se situent dans un intervalle dont les bornes varient selon la fréquence d'observations d'égalité entre les paires, cette mesure a pour avantage de prendre ses valeurs sur (-1;1). Initialement introduite pour modéliser les corrélations entre des variables continues, son extension au cas discret implique certaines restrictions. En effet, la nouvelle mesure pourrait être interprétée comme la corrélation entre les variables aléatoires continues dont la discrétisation constitue nos observations discrètes non négatives. Deux méthodes d'estimation des modèles augmentés en zéro seront présentées dans les contextes fréquentiste et bayésien basées respectivement sur le maximum de vraisemblance et l'intégration de Gauss-Hermite. Enfin, une étude de simulation permet de montrer la robustesse et les limites de notre approche. / This thesis presents some estimation methods and algorithms to analyse count data in particular and discrete data in general. It is also part of an NSERC strategic project, named CC-Bio, which aims to assess the impact of climate change on the distribution of plant and animal species in Québec. After a brief introduction to the concepts and definitions of biogeography and those relative to the generalized linear mixed models in chapters 1 and 2 respectively, my thesis will focus on three major and new ideas. First, we introduce in chapter 3 a new form of distribution whose components have marginal distribution Poisson or Skellam. This new specification allows to incorporate relevant information about the nature of the correlations between all the components. In addition, we present some properties of this probability distribution function. Unlike the multivariate Poisson distribution initially introduced, this generalization enables to handle both positive and negative correlations. A simulation study illustrates the estimation in the two-dimensional case. The results obtained by Bayesian methods via Monte Carlo Markov chain (MCMC) suggest a fairly low relative bias of less than 5% for the regression coefficients of the mean. However, those of the covariance term seem a bit more volatile. Later, the chapter 4 presents an extension of the multivariate Poisson regression with random effects having a gamma density. Indeed, aware that the abundance data of species have a high dispersion, which would make misleading estimators and standard deviations, we introduce an approach based on integration by Monte Carlo sampling. The approach remains the same as in the previous chapter. Indeed, the objective is to simulate independent latent variables to transform the multivariate problem estimation in many generalized linear mixed models (GLMM) with conventional gamma random effects density. While the assumption of knowledge a priori dispersion parameters seems too strong and not realistic, a sensitivity analysis based on a measure of goodness of fit is used to demonstrate the robustness of the method. Finally, in the last chapter, we focus on the definition and construction of a measure of concordance or a correlation measure for some zeros augmented count data with Gaussian copula models. In contrast to Kendall's tau whose values lie in an interval whose bounds depend on the frequency of ties observations, this measure has the advantage of taking its values on the interval (-1, 1). Originally introduced to model the correlations between continuous variables, its extension to the discrete case implies certain restrictions and its values are no longer in the entire interval (-1,1) but only on a subset. Indeed, the new measure could be interpreted as the correlation between continuous random variables before being transformed to discrete variables considered as our discrete non negative observations. Two methods of estimation based on integration via Gaussian quadrature and maximum likelihood are presented. Some simulation studies show the robustness and the limits of our approach.

<p>This thesis discusses novel developments in Bayesian analytics for high-dimensional multivariate time series. The focus is on the class of multiregression dynamic models (MDMs), which can be decomposed into sets of univariate models processed in parallel yet coupled for forecasting and decision making. Parallel processing greatly speeds up the computations and vastly expands the range of time series to which the analysis can be applied. </p><p>I begin by defining a new sparse representation of the dependence between the components of a multivariate time series. Using this representation, innovations involve sparse dynamic dependence networks, idiosyncrasies in time-varying auto-regressive lag structures, and flexibility of discounting methods for stochastic volatilities.</p><p>For exploration of the model space, I define a variant of the Shotgun Stochastic Search (SSS) algorithm. Under the parallelizable framework, this new SSS algorithm allows the stochastic search to move in each dimension simultaneously at each iteration, and thus it moves much faster to high probability regions of model space than does traditional SSS. </p><p>For the assessment of model uncertainty in MDMs, I propose an innovative method that converts model uncertainties from the multivariate context to the univariate context using Bayesian Model Averaging and power discounting techniques. I show that this approach can succeed in effectively capturing time-varying model uncertainties on various model parameters, while also identifying practically superior predictive and lucrative models in financial studies. </p><p>Finally I introduce common state coupled DLMs/MDMs (CSCDLMs/CSCMDMs), a new class of models for multivariate time series. These models are related to the established class of dynamic linear models, but include both common and series-specific state vectors and incorporate multivariate stochastic volatility. Bayesian analytics are developed including sequential updating, using a novel forward-filtering-backward-sampling scheme. Online and analytic learning of observation variances is achieved by an approximation method using variance discounting. This method results in faster computation for sequential step-ahead forecasting than MCMC, satisfying the requirement of speed for real-world applications. </p><p>A motivating example is the problem of short-term prediction of electricity demand in a "Smart Grid" scenario. Previous models do not enable either time-varying, correlated structure or online learning of the covariance structure of the state and observational evolution noise vectors. I address these issues by using a CSCMDM and applying a variance discounting method for learning correlation structure. Experimental results on a real data set, including comparisons with previous models, validate the effectiveness of the new framework.</p> / Dissertation

This research develops a fault diagnosis method for complex systems in the presence of uncertainties and possibility of multiple solutions. Fault diagnosis is a challenging problem because data used in diagnosis contain random errors and often systematic errors as well. Furthermore, fault diagnosis is basically an inverse problem so that it inherits unfavorable characteristics of inverse problems: The existence and uniqueness of an inverse solution are not guaranteed and the solution may be unstable. The weighted least squares method and its variations are traditionally used for solving inverse problems. However, the existing algorithms often fail to identify multiple solutions if they are present. In addition, the existing algorithms are not capable of selecting variables systematically so that they generally use the full model in which may contain unnecessary variables as well as necessary variables. Ignoring this model uncertainty often gives rise to, so called, the smearing effect in solutions, because of which unnecessary variables are overestimated and necessary variables are underestimated. The proposed method solves the inverse problem using Bayesian inference. An engineering system can be parameterized using state variables. The probability of each state variable is inferred from observations made on the system. A bias in an observation is treated as a variable, and the probability of the bias variable is inferred as well. To take the uncertainty of model structure into account, multiple Bayesian models are created with various combinations of the state variables and the bias variables. The results from all models are averaged according to how likely each model is. Gibbs sampling is used for approximating updated probabilities. The method is demonstrated for two applications: the status matching of a turbojet engine and the fault diagnosis of an industrial gas turbine. In the status matching application only physical faults in the components of a turbojet engine are considered whereas in the fault diagnosis application sensor biases are considered as well as physical faults. The proposed method is tested in various faulty conditions using simulated measurements. Results show that the proposed method identifies physical faults and sensor biases simultaneously. It is also demonstrated that multiple solutions can be identified. Overall, there is a clear improvement in ability to identify correct solutions over the full model that contains all state and bias variables.