Statistical Inference for Nonlinear Dynamical Systems

To my family, for their love and support ii ACKNOWLEDGEMENTS This dissertation is the end result of my stay at the University of Michigan during which I have benefited from contact and varied relationships with many members of its community. I thank my advisor Professor Edward Ionides for his patient advice, generosity with his time and for the encouragement to join the statistics research community as a co-author of some of his work. In addition, Professor Ionides recruited me for the cholera project, which has served as a motivation for the statistical results in this dissertation as well as an important funding source throughout the program. I also thank the rest of the people involved in the cholera project, Mercedes Pascual in particular for her role in its organization. Access to Aaron King's cluster of computers has been crucial for reasonable computation times, which have made the whole process substantially more enjoyable. I also thank him for organizing and inviting me to the NCEAS group on inference for dynamical systems. I thank all three for very interesting and stimulating discussions. This dissertation has benefited enormously from the resources that the university provides students with. The faculty and libraries have been a bottomless well of knowledge and the staff at the statistics department kind and helpful. I also thank my fellow graduate students, many of which offered their friendship, help and company in the long hours spent in the shared space. Finally, I would like to add that without the love and support of my family, especially my wife Maria, this thesis would not have been possible. iii Additional acknowledgements are required regarding collaborations. The second chapter has been published, with some minor changes, in the National Proceedings in collaboration with Edward L. Ionides and Aaron A. King. The third and fourth chapters are in the process of being submitted and are in collaboration with Edward