Modeling and Inverse Problems in the Presence of Uncertainty

ISBN: 9780367378752 出版年：2014 页码：403 Banks, H T Hu, Shuhua Thompson, W Clayton CRC Press

Introduction Probability and Statistics Overview Probability and Probability Space Random Variables and Their Associated Distribution Functions Statistical Averages of Random Variables Characteristic Functions of a Random Variable Special Probability Distributions Convergence of a Sequence of Random Variables Mathematical and Statistical Aspects of Inverse Problems Least Squares Inverse Problem Formulations Methodology: Ordinary, Weighted, and Generalized Least Squares Asymptotic Theory: Theoretical Foundations Computation of SIGMAN, Standard Errors, and Confidence Intervals Investigation of Statistical Assumptions Bootstrapping vs. Asymptotic Error Analysis The "Corrective" Nature of Bootstrapping Covariance Estimates and Their Effects on Confidence Intervals Some Summary Remarks on Asymptotic Theory vs. Bootstrapping Model Selection Criteria Introduction Likelihood Based-Model Selection Criteria-Akaike Information Criterion and Its Variations The AIC under the Framework of Least Squares Estimation Example: CFSE Label Decay Residual Sum of Squares Based Model Selection Criterion Estimation of Probability Measures Using Aggregate Population Data Motivation Type I: Individual Dynamics/Aggregate Data Inverse Problems Type II: Aggregate Dynamics/Aggregate Data Inverse Problems Aggregate Data and the Prohorov Metric Framework Consistency of the PMF Estimator Further Remarks Nonparametric Maximum Likelihood Estimation Final Remarks Optimal Design Introduction Mathematical and Statistical Models Algorithmic Considerations Example: HIV Model Propagation of Uncertainty in a Continuous Time Dynamical System Introduction to Stochastic Processes Stochastic Differential Equations Random Differential Equations Relationships between Random and Stochastic Differential Equations A Stochastic System and Its Corresponding Deterministic System Overview of Multivariate Continuous Time Markov Chains Simulation Algorithms for Continuous Time Markov Chain Models Density Dependent Continuous Time Markov Chains and Kurtz's Limit Theorem Biological Application: Vancomycin-Resistant Enterococcus Infection in a Hospital Unit Biological Application: HIV Infection within a Host Application in Agricultural Production Networks Overview of Stochastic Systems with Delays Simulation Algorithms for Stochastic Systems with Fixed Delays Application in the Pork Production Network with a Fixed Delay Simulation Algorithms for Stochastic Systems with Random Delays Application in the Pork Production Network with a Random Delay Frequently Used Notations and Abbreviations Index References appear at the end of each chapter.