Opis: Modeling and Inverse Problems in the Presence of Uncertainty - H. T. Banks, Clayton Thompson, William Clayton Thompson

Modeling and Inverse Problems in the Presence of Uncertainty collects recent research-including the authors' own substantial projects-on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation itself. After a useful review of relevant probability and statistical concepts, the book summarizes mathematical and statistical aspects of inverse problem methodology, including ordinary, weighted, and generalized least-squares formulations. It then discusses asymptotic theories, bootstrapping, and issues related to the evaluation of correctness of assumed form of statistical models. The authors go on to present methods for evaluating and comparing the validity of appropriateness of a collection of models for describing a given data set, including statistically based model selection and comparison techniques. They also explore recent results on the estimation of probability distributions when they are embedded in complex mathematical models and only aggregate (not individual) data are available. In addition, they briefly discuss the optimal design of experiments in support of inverse problems for given models. The book concludes with a focus on uncertainty in model formulation itself, covering the general relationship of differential equations driven by white noise and the ones driven by colored noise in terms of their resulting probability density functions. It also deals with questions related to the appropriateness of discrete versus continuum models in transitions from small to large numbers of individuals. With many examples throughout addressing problems in physics, biology, and other areas, this book is intended for applied mathematicians interested in deterministic and/or stochastic models and their interactions. It is also suitable for scientists in biology, medicine, engineering, and physics working on basic modeling and inverse problems, uncertainty in modeling, propagation of uncertainty, and statistical modeling. "The book is precisely but readable written, uses many examples from practice, and renders information that can be a source of new scientific and applied projects. It is strongly recommended to scientific workers, teachers, and students." -Eduard Kostolansky, Zentralblatt MATH 1296Introduction 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.

Szczegóły: Modeling and Inverse Problems in the Presence of Uncertainty - H. T. Banks, Clayton Thompson, William Clayton Thompson

Tytuł: Modeling and Inverse Problems in the Presence of Uncertainty
Autor: H. T. Banks, Clayton Thompson, William Clayton Thompson
Producent: Apple
ISBN: 9781482206425
Rok produkcji: 2014
Ilość stron: 405
Oprawa: Twarda
Waga: 0.72 kg

Recenzje: Modeling and Inverse Problems in the Presence of Uncertainty - H. T. Banks, Clayton Thompson, William Clayton Thompson