Modeling and inverse problems in the presence of uncertainty
type: Item
instance of: scholarly article
zbMATH Open document ID: 1296.00029
author: W. Clayton Thompson
author: H. Thomas Banks
author: Shuhua Hu
publication date: 2014-01-27T00:00:00Z
Mathematics Subject Classification ID: 00A71
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62-07
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 92-01
zbMATH DE Number: 6250607
zbMATH Keywords: uncertainty
zbMATH Keywords: uncertainty propagation
zbMATH Keywords: inverse problem
zbMATH Keywords: aggregate data
zbMATH Keywords: continuous time Markov chain
zbMATH Keywords: stochastic system
zbMATH Keywords: deterministic system
MaRDI profile type: Publication
full work available at URL: b16760
OpenAlex ID: W1496857014
DOI: 10.1201/B16760
title: Modeling and inverse problems in the presence of uncertainty
published in: Monographs and Research Notes in Mathematics
review text: The book has 391 pages and is broken down into 8 chapters. The introduction specifies two types of problems connected with uncertainty propagation and quantification and are considered in the book. The first problem type includes modeling and inverse problems with a precise mathematical model. The second one assumes that mathematical model is a major source of uncertainty. This chapter in short introduces the book chapter's content. The second chapter describes a must of probability and statistics needed to study the book. Chapter 3 is devoted to mathematical, statistical and computational questions of inverse problems for deterministic dynamical systems using different least squares' methods. Here are also included the asymptotic theory and bootstrapping algorithms. In Chapter 4 are reviewed widely used model selection criteria. Two model types are considered -- a statistical model and a probability distribution model. An introduction to recent results on the estimation of probability distributions that are embedded in complex mathematical models and only aggregate data are available is presented in Chapter 5. Problems on optimal design of experiments (what and when to measure) are shortly described in Chapter 6. Questions of the uncertainty in model construction itself are a subject of Chapter 7. Here, the authors consider uncertainty propagation in a continuous time dynamic system using a stochastic differential equations driven by white noise or a random differential equations driven by other type of random inputs (colored noise). This tool environment supports a study of evolution of probability density functions in time. The last chapter is devoted using continuous time Markov chain models to the problem: a stochastic system and its corresponding deterministic system. 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 the…
description: scientific article; zbMATH DE number 6250607