8:30AM - Halsey Hall, room 120
Multivariate Spline Estimation and Inference for Image-on-scalar regression
Abstract: Motivated by imaging studies in medical and public health research, scientists are interested in understanding how subject-level characteristics, including clinic variables and genetic factors would influence imaging phenotypes. Image-on-scalar regression models are proposed to satisfy this modeling need. Estimating such models is a challenging problem when there exists a fundamental spatial correlation between pixels, organs in biomedical images have an irregular shape and images have various visual qualities.
In this talk, I am going to present a method to simultaneously estimate and make inferences of Image-on-scalar regression models while incorporating the spatial heterogeneity and spatial correlation. First, I will introduce how to use flexible bivariate penalized splines over triangulations (BPST) to estimate the image-on-scalar regression model. The BPST is an effective tool to handle the irregular domain of the objects of interest on the images and other characteristics of images. The proposed estimators of the coefficient functions are proved to be root-n consistent and asymptotically normal under some regularity conditions. Next, I will present a computationally efficient method to conduct statistics inferences for the coefficient functions. Specifically, I will demonstrate how to develop simultaneous confidence corridors (SCCs). A highly efficient and scalable estimation algorithm is developed. The proposed method is applied to the spatially normalized Positron Emission Tomography (PET) data of Alzheimer's Disease Neuroimaging Initiative (ADNI). Finally, I will talk about some future extensions and other related research directions, for instance, when the data is 3d biomedical imaging data. This talk is based on joint work with Prof. Lily Wang, Prof. Guannan Wang, and Prof. Lijian Yang.