Includes bibliographical references and index.
|Statement||Françoise Prêteux, Ali Mohammad-Djafari, Edward R. Dougherty, chairs/editors ; sponsored by SPIE--the International Society for Optical Engineering ; cooperating organization, SIAM--Society for Industrial and Applied Mathematics.|
|Series||SPIE proceedings series ;, v. 3816, Proceedings of SPIE--the International Society for Optical Engineering ;, v. 3816.|
|Contributions||Prêteux, Françoise., Mohammad-Djafari, Ali., Dougherty, Edward R., Society of Photo-optical Instrumentation Engineers., Society for Industrial and Applied Mathematics.|
|LC Classifications||TA1637 .M358 1999|
|The Physical Object|
|Pagination||vii, 334 p. :|
|Number of Pages||334|
|LC Control Number||00266626|
Parameter Estimation and Inverse Problems, 2e provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model. This book takes on these fundamental and challenging problems. Bayesian solutions and performance analysis in bioelectric inverse problems Abstract: In bioelectric inverse problems, one seeks to recover bioelectric sources from remote measurements using a mathematical model that relates the sources to the by: Treating inverse problems from the standpoint of Bayesian estimation has received a significant amount of attention in the literature over the course of the last five years (see, for example, [8,9. The Bayesian estimation procedures outlined above result in a posterior distribution for the MAR coefficients P(W|Y, m).Bayesian inference can then take place using confidence intervals based on this posterior (e.g. see Box and Tiao, ).The posterior allows us to make inferences about the strength of a connection between two regions.
Uncertainty quantification (UQ) is the science of quantitative characterization and reduction of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known. An example would be to predict the acceleration of a human body in a head-on crash with another car: even if we . Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. For the mathematical inverse problem that we obtain after the modeling, we present a uniqueness result, recasting the problem as the recovery of the initial condition for the heat equation in R x (0,∞) from measurements in a space-time curve. Additionally, we present numerical experiments to recover the density of the fluorescent molecules by. The book is devoted entirely to statistical problems for functions, although the treatment is not Bayesian, and the models are somewhat simpler than those arising from PDE problems in the applications which motivate our work; also the function space setting does not play a major role in the approach taken there.
Download PDF Abstract: These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental in the quantification of uncertainty within applications involving the blending of mathematical models . The book is intended for an audience having a solid grounding in probability and statistics at the level of the year-long undergraduate course taken by statistics and mathematics majors. The necessary background on Decision Theory and the frequentist and Bayesian approaches to estimation is presented and carefully discussed in Chapters 1–3. Parameter Estimation and Inverse Problems, 2e provides geoscience students and professionals with answers to common questions like how one can derive a physical model . A biofilm model including quorum sensing and new concept of cooperation is presented. • The effect of uncertainty in the model parameters on biofilms growth is illustrated. • A Bayesian estimation method is proposed to quantify multiple uncertain parameters. • The new biofilm model is verified by comparing the simulations and measurement.