Date of Graduation
Statler College of Engineering and Mineral Resources
Industrial and Managements Systems Engineering
David S Mebane
John A Christian
Numerous engineering problems are concerned with the challenge of representing real life systems through mathematical equations: modeling. Properly generated mathematical models can accurately predict the behavior of natural processes. The key objective of model development is to correctly build a set of equations or expressions that can reproduce the results observed from experimental measurements. By following this methodology, sources of error and uncertainty will arise as most natural processes have random factors that make the results stochastic, and therefore can never be exactly reproduced. A model can try to best approximate the actual outcome, but many times assumptions or simplifications are needed because either the problem becomes mathematically unfeasible, or there is not enough knowledge regarding the process. Additionally, even if models are correctly defined, they may require proper calibration of its parameters to make predictions.;In the study of virology, within host viral infections can be modeled by means of mathematical balances of target cell populations. A virus model will describe how a virus infects healthy cells and spreads by defining a set of depletion/replenishment rate parameters that will depend on each system. The focus of this study is to determine the posterior probability distributions of these parameters that will best approximate a given patient's data, similar to data fitting. Using an inverse modeling approach to generate patient data using known reference values of the virus model parameters and adding random "white" noise, a virus model will be fitted to the generated noisy data using Bayesian methods for parameter estimation.;The main purpose of this study is to validate the use of Bayesian calibration techniques as an alternative to conventional gradient-based parameter estimation methods. The results of a calibrated virus model with a fixed virus generation rate are then used to make model predictions and extrapolate the dynamic behavior to different ranges of the fixed parameter. The results conclude that Bayesian methods can be successfully used for parameter estimation, especially for high-dimensional problems, however the practical identifiability of the parameters is limited by the model's nonlinear terms, the experimental data variance, and the available data measurements. Although the results are encouraging, the excessive computation time needed for obtaining the empirical parameter Posterior distributions limit the practical use of these methods.
Mejia, Alejandro, "Study of Parameter Estimation and Model Calibration Using Bayesian Analysis of Noisy Data for a Virus Model" (2017). Graduate Theses, Dissertations, and Problem Reports. 6211.