Statistical experimental analysis is an indispensable tool in engineering, science, bio-medicine, and technology innovation. There are generally two types of experiments: computer and physical experiments. Computer experiments are simulations using complex mathematical models and numerical tools, while physical experiments are actual experiments performed in a laboratory or observed in the field. Analyzing these experiments helps us understand real-world phenomena and motivates interesting statistical questions and challenges. This thesis presents new methodologies for applications in computer experiments and biomedical studies. In Chapters 1 and 2, we show that the concept of using transformation for improving the additivity of a target function is beneficial in computer experiments and big data modeling. In Chapter 3, motivated by a biological experiment, we propose a new method for quantifying uncertainty in biology studies. Chapter 4 addresses the problem of identifying an optimal computer simulator for the observed physical experiments.Ph.D
