Modeling and inverse problems in the presence of uncertainty
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 scientific workers, teachers and students.
scientific article; zbMATH DE number 6250607