Indiana University-Purdue University Indianapolis (IUPUI) / Joint models of longitudinal and survival outcomes have been used with increasing frequency in clinical investigations. Correct specification of fixed and random effects, as well as their functional forms is essential for practical data analysis. However, no existing methods have been developed to meet this need in a joint model setting. In this dissertation, I describe a penalized likelihood-based method with adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions for model selection. By reparameterizing variance components through a Cholesky decomposition, I introduce a penalty function of group shrinkage; the penalized likelihood is approximated by Gaussian quadrature and optimized by an EM algorithm. The functional forms of the independent effects are determined through a procedure for structural discovery. Specifically, I first construct the model by penalized cubic B-spline and then decompose the B-spline to linear and nonlinear elements by spectral decomposition. The decomposition represents the model in a mixed-effects model format, and I then use the mixed-effects variable selection method to perform structural discovery. Simulation studies show excellent performance. A clinical application is described to illustrate the use of the proposed methods, and the analytical results demonstrate the usefulness of the methods.

The purpose of this thesis is to give an account of the comparable use of dissonance of Palestrina, Lassus, and Victoria through harmonic analysis and statistical comparison, illustrating the stylistic differences among the three composers works. The thesis does. not attempt to cover text setting, melodic construction, ranges, or aesthetic evaluation of composition other than that which pertains to dissonance. The analysis of dissonance was done with primary consideration being given to the vertical structure of the harmony, observing the linear structure only with relation to the approach and resolution of that dissonance.

Model and variable selection have attracted considerable attention in areas of application where datasets usually contain thousands of variables. Variable selection is a critical step to reduce the dimension of high dimensional data by eliminating irrelevant variables. The general objective of variable selection is not only to obtain a set of cost-effective predictors selected but also to improve prediction and prediction variance. We have made several contributions to this issue through a range of advanced topics: providing a graphical view of Bayesian Variable Selection (BVS), recovering sparsity in multivariate nonparametric models and proposing a testing procedure for evaluating nonlinear interaction effect in a semiparametric model. To address the first topic, we propose a new Bayesian variable selection approach via the graphical model and the Ising model, which we refer to the ``Bayesian Ising Graphical Model'' (BIGM). There are several advantages of our BIGM: it is easy to (1) employ the single-site updating and cluster updating algorithm, both of which are suitable for problems with small sample sizes and a larger number of variables, (2) extend this approach to nonparametric regression models, and (3) incorporate graphical prior information. In the second topic, we propose a Nonnegative Garrote on a Kernel machine (NGK) to recover sparsity of input variables in smoothing functions. We model the smoothing function by a least squares kernel machine and construct a nonnegative garrote on the kernel model as the function of the similarity matrix. An efficient coordinate descent/backfitting algorithm is developed. The third topic involves a specific genetic pathway dataset in which the pathways interact with the environmental variables. We propose a semiparametric method to model the pathway-environment interaction. We then employ a restricted likelihood ratio test and a score test to evaluate the main pathway effect and the pathway-environment interaction. / Ph. D.