Natural scene statistics (NSS) have played an increasingly important role in both our understanding of the function and evolution of the human vision system, and in the development of modern image processing applications. Because depth/range, i.e., egocentric distance, is arguably the most important thing a visual system must compute (from an evolutionary perspective), the joint statistics between natural image and depth/range information are of particular interest. However, while there exist regular and reliable statistical models of two-dimensional (2D) natural images, there has been little work done on statistical modeling of natural luminance/chrominance and depth/disparity, and of their mutual relationships. One major reason is the dearth of high-quality three-dimensional (3D) image and depth/range database. To facilitate research progress on 3D natural scene statistics, this dissertation first presents a high-quality database of color images and accurately co-registered depth/range maps using an advanced laser range scanner mounted with a high-end digital single-lens reflex camera. By utilizing this high-resolution, high-quality database, this dissertation performs reliable and robust statistical modeling of natural image and depth/disparity information, including new bivariate and spatial oriented correlation models. In particular, these new statistical models capture higher-order dependencies embedded in spatially adjacent bandpass responses projected from natural environments, which have not yet been well understood or explored in literature. To demonstrate the efficacy and effectiveness of the advanced NSS models, this dissertation addresses two challenging, yet very important problems, depth estimation from monocular images and no-reference stereoscopic/3D (S3D) image quality assessment. A Bayesian depth estimation framework is proposed to consider the canonical depth/range patterns in natural scenes, and it forms priors and likelihoods using both univariate and bivariate NSS features. The no-reference S3D image quality index proposed in this dissertation exploits new bivariate and correlation NSS features to quantify different types of stereoscopic distortions. Experimental results show that the proposed framework and index achieve superior performance to state-of-the-art algorithms in both disciplines. / text

Vitamin K has a negligible effect on bone mineral density (BMD) and a large but uncertain effect on fractures. The three studies in the thesis explored uncertainty about the effect of vitamin K on fractures using the methods of economic evaluation and Bayesian meta-analysis. In study 1, a Markov probabilistic microsimulation model was developed for a hypothetical cohort of 50-year-old postmenopausal women without osteoporosis. This was a fracture incidence-based model, populated with data from the literature. It was used to examine the cost-effectiveness of two supplementation strategies over a lifetime horizon. We compared vitamin K2 (or vitamin K1) concurrent with vitamin D3 and calcium versus vitamin D3 and calcium alone. Study 2 included a systematic review, and classical and Bayesian univariate meta-analyses to determine the efficacies of the K vitamins on BMD or fractures in current and future trials. Study 3 used Bayesian bivariate random-effects meta-analysis to jointly model the treatment effects on two correlated bone outcomes. We compared the estimates from the univariate and bivariate meta-analyses and explored how these results would change the conclusions of the cost-effectiveness analysis. The strategies including vitamin K were highly cost-effective at willingness-to-pay of $50,000/QALY (quality-adjusted life year); however, the results were most sensitive to changes in the efficacy of vitamin K. The univariate meta-analyses showed large uncertainties in the anti-fracture effects of vitamin K2 in current and future trials. The bivariate 95% credible intervals were considerably narrower than those from the univariate meta-analyses. Using future odds ratios from the bivariate meta-analyses, vitamin K2 cost more than $100,000/QALY while vitamin K1 was cost-saving. Our analyses found substantial uncertainty around the estimates of the vitamin K effect on fractures. We recommend against routine use of vitamin K for fracture prevention. Bayesian bivariate meta-analysis accounts for all available information and should be considered when the treatment effects are measured on two correlated outcomes.

Vitamin K has a negligible effect on bone mineral density (BMD) and a large but uncertain effect on fractures. The three studies in the thesis explored uncertainty about the effect of vitamin K on fractures using the methods of economic evaluation and Bayesian meta-analysis. In study 1, a Markov probabilistic microsimulation model was developed for a hypothetical cohort of 50-year-old postmenopausal women without osteoporosis. This was a fracture incidence-based model, populated with data from the literature. It was used to examine the cost-effectiveness of two supplementation strategies over a lifetime horizon. We compared vitamin K2 (or vitamin K1) concurrent with vitamin D3 and calcium versus vitamin D3 and calcium alone. Study 2 included a systematic review, and classical and Bayesian univariate meta-analyses to determine the efficacies of the K vitamins on BMD or fractures in current and future trials. Study 3 used Bayesian bivariate random-effects meta-analysis to jointly model the treatment effects on two correlated bone outcomes. We compared the estimates from the univariate and bivariate meta-analyses and explored how these results would change the conclusions of the cost-effectiveness analysis. The strategies including vitamin K were highly cost-effective at willingness-to-pay of $50,000/QALY (quality-adjusted life year); however, the results were most sensitive to changes in the efficacy of vitamin K. The univariate meta-analyses showed large uncertainties in the anti-fracture effects of vitamin K2 in current and future trials. The bivariate 95% credible intervals were considerably narrower than those from the univariate meta-analyses. Using future odds ratios from the bivariate meta-analyses, vitamin K2 cost more than $100,000/QALY while vitamin K1 was cost-saving. Our analyses found substantial uncertainty around the estimates of the vitamin K effect on fractures. We recommend against routine use of vitamin K for fracture prevention. Bayesian bivariate meta-analysis accounts for all available information and should be considered when the treatment effects are measured on two correlated outcomes.

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Different universal (also called automatic or black-box) methods have been suggested to sample from univariate log-concave distributions. The description of a universal generator for bivariate distributions has not been published up to now. The new algorithm for bivariate log-concave distributions is based on the method of transformed density rejection. In order to construct a hat function for a rejection algorithm the bivariate density is transformed by the logarithm into a concave function. Then it is possible to construct a dominating function by taking the minimum of several tangent planes which are by exponentiation transformed back into the original scale. The choice of the points of contact is automated using adaptive rejection sampling. This means that a point that is rejected by the rejection algorithm is used as additional point of contact until the maximal number of points of contact is reached. The paper describes the details how this main idea can be used to construct Algorithm ULC2D that can generate random pairs from bivariate log-concave distribution with a computable density. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Amplitude Variation with Oset (AVO) inversion is one of the techniques that is being used to estimate subsurface physical parameters such as P-wave velocity, S-wave velocity, and density or their attributes. AVO inversion is an ill-conditioned problem which has to be regularized in order to obtain a stable and unique solution. In this thesis, a Bayesian procedure that uses a Multivariate Cauchy distribution as a prior probability distribution is introduced. The prior includes a scale matrix that imposes correlation among the AVO attributes and induces a regularization that provokes solutions that are sparse and stable in the presence of noise. The performance of this regularization is demonstrated by both synthetic and real data examples using linearized approximations to the Zoeppritz equations. / Geophysics

In this thesis, we introduce a concept of directional quantile envelopes, the intersection of the halfspaces determined by directional quantiles, and show that they allow for explicit probabilistic interpretation, compared to other multivariate quantile concepts. Directional quantile envelopes provide a way to perform multivariate quantile regression: to ``regress contours'' on covariates. We also develop theory and algorithms for an important application of multivariate quantile regression in biometry: bivariate growth charts. We prove that directional quantiles are continuous and derive their closed-form expression for elliptically symmetric distributions. We provide probabilistic interpretations of directional quantile envelopes and establish that directional quantile envelopes are essentially halfspace depth contours. We show that distributions with smooth directional quantile envelopes are uniquely determined by their envelopes. We describe an estimation scheme of directional quantile envelopes and prove its affine equivariance. We establish the consistency of the estimates of directional quantile envelopes and describe their accuracy. The results are applied to estimation of bivariate extreme quantiles. One of the main contributions of this thesis is the construction of bivariate growth charts, an important application of multivariate quantile regression. We discuss the computation of our multivariate quantile regression by developing a fast elimination algorithm. The algorithm constructs the set of active halfspaces to form a directional quantile envelope. Applying this algorithm to a large number of quantile halfspaces, we can construct an arbitrary exact approximation of the direction quantile envelope. In the remainder of the thesis, we exhibit the connection between depth contours and directional regression quantiles (Laine, 2001), stated without proof in Koenker (2005). Our proof uses the duality theory of primal-dual linear programming. Aiming at interpreting halfspace depth contours, we explore their properties for empirical distributions, absolutely continuous distributions and certain general distributions. Finally, we propose a generalized quantile concept, depth quantile, inspired by halfspace depth (Tukey, 1975) and regression depth (Rousseeuw and Hubert, 1999). We study its properties in various data-analytic situations: multivariate and univariate locations, regression with and without intercept. In the end, we show an example that while the quantile regression of Koenker and Bassett (1978) fails, our concept provides sensible answers. / Statistics

Household survey data collected primarily from rural Bangladesh (Multiple Indicator Cluster Survey 2005-2006) is utilized in this paper to identify the important individual, household and district-level factors that influence the decision making process that parents undertake to determine their children’s (between the age of 7 and 14 inclusive) absence rate from school and work intensity. Bivariate Tobit model is used to jointly estimate the absence rate and hours worked equations. The results of the analysis conducted in this paper suggest that an increase in perceived returns on human capital from attending school – as measured by the wage differential between low-skilled and higher-skilled occupations in a given market – negatively impact absence rate in rural Bangladesh. Moreover, results suggest that the education level of the parents has an impact on a child’s absence rate and the number of hours worked in a week. It is found that the higher the education level of the father, the lower the absence rate and the number of hours worked of a child, while higher levels of the mother’s education level is shown to negatively impact the absence rate. It is also found that being the first born child in a household is associated with both higher absence rate from school and greater amount of hours worked per week. With respect to gender, being a girl is found to be associated with a greater number of hours worked. Lastly, household wealth is found to have a U-shaped relationship with both absence rates and number of hours worked; it is negatively associated with both of the dependent variables at lower levels, but has a positive impact on both absence rate and number of hours worked at higher levels. In general, the results detailed in this paper highlight the importance of policies such as the provision of cash stipends to the poorest households, improving the quality of schooling facilities and directed educational schemes meant to eradicate the persistent gender inequality that is hindering truly universal primary education in rural Bangladesh. / Graduate / 0501 / najsaqib@hotmail.com

Notre objectif de ce travail est d’étudier l’efficience du marché financier tunisien avant et après la révolution de Jasmin de 2011 et de déterminer les facteurs macroéconomiques et financiers qui influencent le score d’efficience de ce marché. Notre méthodologie consiste à utiliser dans un premier temps le modèle GARCH multivarié pour estimer le coefficient de corrélation entre les rendements du marché et ceux des différentes banques et le coefficient Béta. Comme ce modèle suppose des résidus qui suivent la loi normale multivariée qui est une hypothèse non vérifiée dans la pratique, nous allons utiliser dans un deuxième temps la théorie des copules pour donner une plus grande souplesse dans la modélisation des données multivariées. Les facteurs les plus influents sont déterminés en utilisant le modèle de régression linéaire,le modèle de données de Panel et le modèle TOBIT. Les résultats empiriques montrent que le marché tunisien n’est pas efficient ni avant ni après la révolution. Beaucoup d’actions sont proposées pour améliorer le degré d’efficience de ce marché. / Our objective of this work is to study the efficiency of the Tunisian financial market before and after the Jasmin revolution of 2011 and identify macro-economic and financial factors that influence the efficiency score of this market. Our methodology is to use at first multivariate GARCH model to estimate the correlation between market returns and those of individual banks and the Beta coefficient. As this model assumes the residues that follow the multivariate normal law is untested in practice, we used in a second step the copula theory to provide more flexibility in modeling multivariate data. The most influential factors are determined using the linear regression model, the panel data model and TOBIT model. The empirical results show that the Tunisian market is not efficient either before or after the revolution. Many actions are proposed to improve the degree of efficiency of this market.