We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompass many stud...

The question of how populations of neurons process information is not fully understood yet. With the advent of new experimental techniques, however, it becomes possible to measure a great number of neurons simultaneously. As a result, models of co-variation of neurons are becoming increasingly important. In this thesis new methods are introduced for analyzing the importance of stochastic depend...

For random variables with Archimedean copula or survival copula, we develop the reversed hazard rate order and the hazard rate order on sample extremes in the context of proportional reversed hazard models and proportional hazard models, respectively. The likelihood ratio order on sample maximum is also investigated for the proportional reversed hazard model. Several numerical examples are pres...

Goodness-of-fit tests are a fundamental element in the copula-based modeling of multivariate continuous distributions. Among the different procedures proposed in the literature, recent large scale simulations suggest that one of the most powerful tests is based on the empirical process comparing the empirical copula with a parametric estimate of the copula derived under the null hypothesis. As ...

One approach for constructing copula functions is by multiplication. Given that products of cumulative distribution functions (CDFs) are also CDFs, an adjustment to this multiplication will result in a copula model, as discussed by Liebscher (J Mult Analysis, 2008). Parameterizing models via products of CDFs has some advantages, both from the copula perspective (e.g., it is well-defined for any...

Copula has become a standard tool in describing dependent relations between random variables. This paper proposes a nonparametric bivariate copula estimation method based on shape-restricted -support vector regression ( -SVR). This method explicitly supplements the classical -SVR with constraints related to three shape restrictions: grounded, marginal and 2-increasing, which are the necessary a...

We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models (CGGMs) and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompass m...