Modeling and Inverse Problems in the Presence of Uncertainty - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Modeling and Inverse Problems in the Presence of Uncertainty write by H. T. Banks. This book was released on 2014-04-01. Modeling and Inverse Problems in the Presence of Uncertainty available in PDF, EPUB and Kindle. 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.
Inverse Problems, Control and Modeling in the Presence of Uncertainty
Inverse Problems, Control and Modeling in the Presence of Uncertainty - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Inverse Problems, Control and Modeling in the Presence of Uncertainty write by Harvey Thomas Banks. This book was released on 2007. Inverse Problems, Control and Modeling in the Presence of Uncertainty available in PDF, EPUB and Kindle. We report progress on the development of methods in a number of specific areas of application including static, non-cooperative games related to counter- and counter-counter-electromagnetic interrogation of targets, modeling of complex viscoelastic polymeric materials, stochastic and deterministic models for complex networks and development of inverse problem methodologies (generalized sensitivity functions; asymptotic standard errors) for estimation of infinite dimensional functional parameters including probability measures and temporal/spatial dependent functions in complex nonlinear dynamical systems. These efforts are part of our fundamental research in a modeling, estimation and control methodology (theoretical, statistical and computational) for systems in the presence of major model and observation uncertainties.
Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems
Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems write by Chakraverty, S.. This book was released on 2014-01-31. Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems available in PDF, EPUB and Kindle. "This book provides the reader with basic concepts for soft computing and other methods for various means of uncertainty in handling solutions, analysis, and applications"--Provided by publisher.
Large-Scale Inverse Problems and Quantification of Uncertainty
Large-Scale Inverse Problems and Quantification of Uncertainty - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Large-Scale Inverse Problems and Quantification of Uncertainty write by Lorenz Biegler. This book was released on 2010-11-15. Large-Scale Inverse Problems and Quantification of Uncertainty available in PDF, EPUB and Kindle. This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: • Brings together the perspectives of researchers in areas of inverse problems and data assimilation. • Assesses the current state-of-the-art and identify needs and opportunities for future research. • Focuses on the computational methods used to analyze and simulate inverse problems. • Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Inverse Problem Theory and Methods for Model Parameter Estimation write by Albert Tarantola. This book was released on 2005-01-01. Inverse Problem Theory and Methods for Model Parameter Estimation available in PDF, EPUB and Kindle. While the prediction of observations is a forward problem, the use of actual observations to infer the properties of a model is an inverse problem. Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role in the theory, which is based on probability theory. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, and many of the arguments are heuristic.
