Date of Award

Fall 2014

Degree Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Gregery T. Buzzard

Committee Chair

Gregery T. Buzzard

Committee Member 1

Ann E. Rundell

Committee Member 2

Zhilan Feng

Committee Member 3

Guang Lin


Despite the ever-increasing interest in understanding biology at the system level, there are several factors that hinder studies and analyses of biological systems. First, unlike systems from other applied fields whose parameters can be effectively identified, biological systems are usually unidentifiable, even in the ideal case when all possible system outputs are known with high accuracy. Second, the presence of multivariate bifurcations often leads the system to behaviors that are completely different in nature. In such cases, system outputs (as function of parameters/inputs) are usually discontinuous or have sharp transitions across domains with different behaviors. Finally, models from systems biology are usually strongly nonlinear with large numbers of parameters and complex interactions. This results in high computational costs of model simulations that are required to study the systems, an issue that becomes more and more problematic when the dimensionality of the system increases. Similarly, wet-lab experiments to gather information about the biological model of interest are usually strictly constrained by research budget and experimental settings. The choice of experiments/simulations for inference, therefore, needs to be carefully addressed. ^ The work presented in this dissertation develops strategies to address theoretical and practical limitations in uncertainty quantification and experimental design of non-linear mathematical models, applied in the context of systems biology. This work resolves those issues by focusing on three separate but related approaches: (i) the use of probabilistic frameworks for uncertainty quantification in the face of unidentifiability (ii) the use of behavior discrimination algorithms to study systems with discontinuous model responses and (iii) the use of effective sampling schemes and optimal experimental design to reduce the computational/experimental costs. ^ This cumulative work also places strong emphasis on providing theoretical foundations for the use of the proposed framework: theoretical properties of algorithms at each step in the process are investigated carefully to give more insights about how the algorithms perform, and in many cases, to provide feedback to improve the performance of existing approaches. Through the newly developed procedures, we successfully created a general probabilistic framework for uncertainty quantification and experiment design for non-linear models in the face of unidentifiability, sharp model responses with limited number of model simulations, constraints on experimental setting, and even in the absence of data. The proposed methods have strong theoretical foundations and have also proven to be effective in studies of expensive high-dimensional biological systems in various contexts.