Novel Statistical Methodologies for the Analysis of Computer and Biology Experiments

Abstract

In this talk, I will present two new methodologies used for computer and biology Experiments. In computer experiments, Gaussian process (GP) is a popular choice for approximating a deterministic function, but the role of transformation in GP modeling is not well understood. I will argue that using a transformation on the response can make the deterministic function approximately additive, which can then be easily estimated using an additive GP. Such a GP is named as Transformed Additive Gaussian (TAG) process. I will explain efficient techniques for fitting a TAG process and the advantages of using TAG. Some extensions of TAG for modeling large-scaled and high dimensional data will also be discussed. The second methodology is motivated by a biology experiment in the study of T cell signaling. The biology experiments possess some common features in many applications, such as random effects and varying coefficients, but a method that can quantify the features has not yet been systematically developed in the literature. To fill in the research gap, we propose the local linear varying coefficient frailty method. The method provides a rigorous quantification of an early and rapid impact on T cell signaling from the accumulation of bond lifetime, which can shed new light on the fundamental understanding of how T cells initiate immune responses.? The theoretical properties of the estimators from the method, including the bias correction property near the boundary, will be presented along with discussions on the asymptotic bias-variance trade-off.