This thesis consists of two parts. The first part focuses on design and analysis for computer experiments and the second part deals with binary time series and its application to kinetic studies in micropipette experiments. The first part of the thesis addresses three problems. The first problem is concerned with optimal design of computer experiments. Latin hypercube designs (LHDs) have been used extensively for computer experiments. A multi-objective optimization approach is proposed to find good LHDs by combining correlation and distance performance measures. Several examples are presented to show that the obtained designs are good in terms of both criteria. The second problem is related to the analysis of computer experiments. Kriging is the most popular method for approximating complex computer models. Here a modified kriging method is proposed, which has an unknown mean model. Therefore it is called blind kriging. The unknown mean model is identified from experimental data using a Bayesian variable selection technique. Many examples are presented which show remarkable improvement in prediction using blind kriging over ordinary kriging. The third problem is related to computer experiments with nested and branching factors. Design and analysis of experiments with branching and nested factors are challenging and have not received much attention in the literature. Motivated by a computer experiment in a machining process, we develop optimal LHDs and kriging methods that can accommodate branching and nested factors. Through the application of the proposed methods, optimal machining conditions and tool edge geometry are attained, which resulted in a remarkable improvement in the machining process. The second part of the thesis deals with binary time series analysis with application to cell adhesion frequency experiments. Motivated by the analysis of repeated adhesion tests, a binary time series model incorporating random effects is developed in this chapter. A goodness-of-fit statistic is introduced to assess the adequacy of distribution assumptions on the dependent binary data with random effects. Application of the proposed methodology to real data from a T-cell experiment reveals some interesting information. These results provide some quantitative evidence to the speculation that cells can have ¡§memory¡¨ in their adhesion behavior.

The purpose of this monograph is to make a detailed study about studying of relations. So, we will provide some definitions. Developing this Themes like binary relations, equivalence relations and order relations. At the same we will show ways to represent relations highlighting the representation in the form of graphs. And we will finish the job with Topological Ordering in completing some tasks of a project. / O objetivo desta monografia é fazer um estudo detalhado sobre relações. Para tanto, forneceremos algumas definições. Para o desenvolvimento deste foram abordados temas como relações binárias, relações de equivalência e relações de ordem. No desenvolvimento deste veremos formas de representar as relações dando destaque a representação na forma de Grafos. E finalizamos o trabalho com a Ordenação Topológica na conclusão de algumas tarefas de um projeto.

The purpose of this monograph is to make a detailed study about studying of relations. So, we will provide some definitions. Developing this Themes like binary relations, equivalence relations and order relations. At the same we will show ways to represent relations highlighting the representation in the form of graphs. And we will finish the job with Topological Ordering in completing some tasks of a project. / O objetivo desta monografia é fazer um estudo detalhado sobre relações. Para tanto, forneceremos algumas definições. Para o desenvolvimento deste foram abordados temas como relações binárias, relações de equivalência e relações de ordem. No desenvolvimento deste veremos formas de representar as relações dando destaque a representação na forma de Grafos. E finalizamos o trabalho com a Ordenação Topológica na conclusão de algumas tarefas de um projeto.

Multiple-outcome longitudinal data are abundant in clinical investigations. For example, infections with different pathogenic organisms are often tested concurrently, and assessments are usually taken repeatedly over time. It is therefore natural to consider a multivariate modeling approach to accommodate the underlying interrelationship among the multiple longitudinally measured outcomes. This dissertation proposes a multivariate semiparametric modeling framework for such data. Relevant estimation and inference procedures as well as model selection tools are discussed within this modeling framework. The first part of this research focuses on the analytical issues concerning binary data. The second part extends the binary model to a more general situation for data from the exponential family of distributions. The proposed model accounts for the correlations across the outcomes as well as the temporal dependency among the repeated measures of each outcome within an individual. An important feature of the proposed model is the addition of a bivariate smooth function for the depiction of concurrent nonlinear and possibly interacting influences of two independent variables on each outcome. For model implementation, a general approach for parameter estimation is developed by using the maximum penalized likelihood method. For statistical inference, a likelihood-based resampling procedure is proposed to compare the bivariate nonlinear effect surfaces across the outcomes. The final part of the dissertation presents a variable selection tool to facilitate model development in practical data analysis. Using the adaptive least absolute shrinkage and selection operator (LASSO) penalty, the variable selection tool simultaneously identifies important fixed effects and random effects, determines the correlation structure of the outcomes, and selects the interaction effects in the bivariate smooth functions. Model selection and estimation are performed through a two-stage procedure based on an expectation-maximization (EM) algorithm. Simulation studies are conducted to evaluate the performance of the proposed methods. The utility of the methods is demonstrated through several clinical applications.