Document Type

Dissertation

Date of Degree

Summer 2016

Degree Name

PhD (Doctor of Philosophy)

Degree In

Statistics

First Advisor

Kung-Sik Chan

Abstract

In this study, we aim to develop new likelihood based method for estimating parameters of ordinary differential equations (ODEs) / delay differential equations (DDEs) models. Those models are important for modeling dynamical processes that are described in terms of their derivatives and are widely used in many fields of modern science, such as physics, chemistry, biology and social sciences. We use our new approach to study a distributed delay differential equation model, the statistical inference of which has been unexplored, to our knowledge. Estimating a distributed DDE model or ODE model with time varying coefficients results in a large number of parameters. We also apply regularization for efficient estimation of such models. We assess the performance of our new approaches using simulation and applied them to analyzing data from epidemiology and ecology.

Keywords

Delay Differential Equation, Epidemiology, Generalized Profiling, SPARSE REGULARIZATION, Time Varying Parameters

Pages

ix, 116

Bibliography

112-116

Copyright

Copyright 2016 Ziqian Zhou

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