Stochastic Dynamic Models for Functional Data

To my parents and zhenzhen ii ACKNOWLEDGEMENTS I would like to express my deepest gratitude to my advisors Jeremy Taylor and Peter Song for supporting me to explore this research topic and for advising my dissertation work along the way. Their broad knowledge and attitude towards research will serve as academic role models for me. I also appreciate Morton Brown and Jeremy Taylor for providing my financial support and letting me be involved several interesting collaborative research projects. I am grateful to Naisyin Wang and Brisa Sanchez for serving as my dissertation committee. Their advice and comments are so valuable. I would like to thank all faculty members of the Department of Biostatistics for teaching me biostatistics. I have taken many great classes, especially 699, and have had a lot of valuable discussions with my teachers and my classmates. I have spent my most wonderful time at the Department of Biostatistics at th