Uncertainty Analysis of Biological Nonlinear Models Based on Bayesian Estimation

Abstract

The general goal of this study is to develop an uncertainty analysis procedure based on realistic distribution for nonlinear models, especially biological models. Parameter estimation, random number generation, and uncertainty analysis are closely related in Monte Carlo simulation based model assessment. All three aspects are discussed in this study. Because of the complexity of models and inflexibility of estimation methods, existing estimation methods can not properly estimate the parameters of nonlinear biological models. Assessment of these models is based on unrealistic independent distribution of the parameters. Model assessment may provide incorrect information when parameter distribution is not realistic. In this study, Bayesian estimation with rejection sampling has been extended to estimate the parameters of nonlinear models. This estimation method can estimate marginal distributions and correlation among all parameters of nonlinear models. A sampling algorithm, Conditional Independent Sampling, has been developed to increase sampling efficiency and to increase the accuracy of the generated random samples. An uncertainty analysis method based on improved Monte Carlo has also been developed to fit the characteristics of the correlated joint distribution in establishing error budgets. The model assessment based on this method is very close to that based on crude Monte Carlo. The error budgets based on realistic correlated distribution are much more reasonable compared to those based on assumed independent distribution. The capability and flexibility of these alternative methods have been demonstrated by applications.