Modeling Uncertainty In Metric Space

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Modeling Uncertainty In Metric Space

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Author : Kwangwon Park
language : en
Publisher: Stanford University
Release Date : 2011

Modeling Uncertainty In Metric Space written by Kwangwon Park and has been published by Stanford University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.

Modeling uncertainty for future prediction requires drawing multiple posterior models. Such drawing within a Bayesian framework is dependent on the likelihood (data-model relationship) as well as prior distribution of the model variables, For the uncertainty assessment in the Earth models, we propose the framework of Modeling Uncertainty in Metric Space (MUMS) to achieve this in a general way. MUMS constructs a metric space where the models are represented exclusively by a distance correlated with or equal to the difference in their responses (application-tailored distance). In the framework of MUMS, various operations are available: projection of metric space by multi-dimensional scaling, model expansion by kernel Karhunen-Loeve expansion, generation of additional prior model by solving the pre-image problem, and generation of multiple posterior models by solving the post-image problem. We propose a robust solution for the pre-image problem: geologically constrained optimization, which utilizes the probability perturbation method from the solution of the fixed-point iteration algorithm. Additionally, we introduce a so-called post-image problem for obtaining the feature expansion of the ''true Earth'' by defining a distance as the difference in their responses. The combination of geologically constrained optimization and the post-image problem efficiently generates multiple posterior Earth models constrained to prior geologic information, hard data, and nonlinear time-dependent data. The proposed method provides a realistic uncertainty model for future prediction, compared with the result of the rejection sampler. We also propose a metric ensemble Kalman filter (Metric EnKF), which applies the ensemble Kalman filter (EnKF) to the parameterizations by the kernel KL expansion in metric space. Metric EnKF overcomes some critical limitations of EnKF: it preserves prior geologic information; it creates a stable and consistent filtering. However, the results of Metric EnKF applied to various cases including the Brugge field-scale synthetic reservoir show the same problem as with the EnKF in general, that is, it does not provide a realistic uncertainty model.

Modeling Uncertainty In Metric Space

DOWNLOAD
Author : Kwangwon Park
language : en
Publisher:
Release Date : 2011

Modeling Uncertainty In Metric Space written by Kwangwon Park and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.

Modeling uncertainty for future prediction requires drawing multiple posterior models. Such drawing within a Bayesian framework is dependent on the likelihood (data-model relationship) as well as prior distribution of the model variables, For the uncertainty assessment in the Earth models, we propose the framework of Modeling Uncertainty in Metric Space (MUMS) to achieve this in a general way. MUMS constructs a metric space where the models are represented exclusively by a distance correlated with or equal to the difference in their responses (application-tailored distance). In the framework of MUMS, various operations are available: projection of metric space by multi-dimensional scaling, model expansion by kernel Karhunen-Loeve expansion, generation of additional prior model by solving the pre-image problem, and generation of multiple posterior models by solving the post-image problem. We propose a robust solution for the pre-image problem: geologically constrained optimization, which utilizes the probability perturbation method from the solution of the fixed-point iteration algorithm. Additionally, we introduce a so-called post-image problem for obtaining the feature expansion of the ''true Earth'' by defining a distance as the difference in their responses. The combination of geologically constrained optimization and the post-image problem efficiently generates multiple posterior Earth models constrained to prior geologic information, hard data, and nonlinear time-dependent data. The proposed method provides a realistic uncertainty model for future prediction, compared with the result of the rejection sampler. We also propose a metric ensemble Kalman filter (Metric EnKF), which applies the ensemble Kalman filter (EnKF) to the parameterizations by the kernel KL expansion in metric space. Metric EnKF overcomes some critical limitations of EnKF: it preserves prior geologic information; it creates a stable and consistent filtering. However, the results of Metric EnKF applied to various cases including the Brugge field-scale synthetic reservoir show the same problem as with the EnKF in general, that is, it does not provide a realistic uncertainty model.

Modeling Uncertainty In The Earth Sciences

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Author : Jef Caers
language : en
Publisher: John Wiley & Sons
Release Date : 2011-05-25

Modeling Uncertainty In The Earth Sciences written by Jef Caers and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-25 with Science categories.

Modeling Uncertainty in the Earth Sciences highlights the various issues, techniques and practical modeling tools available for modeling the uncertainty of complex Earth systems and the impact that it has on practical situations. The aim of the book is to provide an introductory overview which covers a broad range of tried-and-tested tools. Descriptions of concepts, philosophies, challenges, methodologies and workflows give the reader an understanding of the best way to make decisions under uncertainty for Earth Science problems. The book covers key issues such as: Spatial and time aspect; large complexity and dimensionality; computation power; costs of 'engineering' the Earth; uncertainty in the modeling and decision process. Focusing on reliable and practical methods this book provides an invaluable primer for the complex area of decision making with uncertainty in the Earth Sciences.

Advances In Soft Computing Intelligent Robotics And Control

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Author : János Fodor
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-03-20

Advances In Soft Computing Intelligent Robotics And Control written by János Fodor and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-20 with Technology & Engineering categories.

Soft computing, intelligent robotics and control are in the core interest of contemporary engineering. Essential characteristics of soft computing methods are the ability to handle vague information, to apply human-like reasoning, their learning capability and ease of application. Soft computing techniques are widely applied in the control of dynamic systems, including mobile robots. The present volume is a collection of 20 chapters written by respectable experts of the fields, addressing various theoretical and practical aspects in soft computing, intelligent robotics and control. The first part of the book concerns with issues of intelligent robotics, including robust xed point transformation design, experimental verification of the input-output feedback linearization of differentially driven mobile robot and applying kinematic synthesis to micro electro-mechanical systems design. The second part of the book is devoted to fundamental aspects of soft computing. This includes practical aspects of fuzzy rule interpolation, subjective weights based meta learning in multi criteria decision making, swarm-based heuristics for an area exploration and knowledge driven adaptive product representations. The last part addresses different problems, issues and methods of applied mathematics. This includes perturbation estimates for invariant subspaces of Hessenberg matrices, uncertainty and nonlinearity modelling by probabilistic metric spaces and comparison and visualization of the DNA of six primates.

Handbook Of Geomathematics

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Author : Willi Freeden
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-13

Handbook Of Geomathematics written by Willi Freeden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-13 with Mathematics categories.

During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.

Pattern Theory

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Author : Ulf Grenander
language : en
Publisher: OUP Oxford
Release Date : 2006-12-14

Pattern Theory written by Ulf Grenander and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-14 with Technology & Engineering categories.

Pattern Theory: From Representation to Inference provides a comprehensive and accessible overview of the modern challenges in signal, data and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website. The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via conditioning structure and Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn, and Chapters 10, 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy, and finally Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.

Model Validation And Uncertainty Quantification Volume 3

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Author : Robert Barthorpe
language : en
Publisher: Springer
Release Date : 2018-07-30

Model Validation And Uncertainty Quantification Volume 3 written by Robert Barthorpe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-30 with Technology & Engineering categories.

Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018, the third volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Uncertainty Quantification in Material Models Uncertainty Propagation in Structural Dynamics Practical Applications of MVUQ Advances in Model Validation & Uncertainty Quantification: Model Updating Model Validation & Uncertainty Quantification: Industrial Applications Controlling Uncertainty Uncertainty in Early Stage Design Modeling of Musical Instruments Overview of Model Validation and Uncertainty

An Introduction To Mathematical Analysis For Economic Theory And Econometrics

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Author : Dean Corbae
language : en
Publisher: Princeton University Press
Release Date : 2009-02-17

An Introduction To Mathematical Analysis For Economic Theory And Econometrics written by Dean Corbae and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-17 with Business & Economics categories.

Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory

Catastrophes And Unexpected Behavior Patterns In Complex Artificial Populations

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Author : Stanislaw Raczynski
language : en
Publisher: Springer Nature
Release Date : 2021-07-05

Catastrophes And Unexpected Behavior Patterns In Complex Artificial Populations written by Stanislaw Raczynski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-05 with Business & Economics categories.

A major objective of this monograph is to present an agent-based simulation of artificial populations. The focus is on possible unexpected or catastrophic events that may spontaneously appear in simulations. A short recall of the tenets of the theory of catastrophes is given. Several examples of artificial society simulations are provided as the main topic of the book. With agent-based modeling, possible catastrophes and unexpected events in artificial populations are simulated. The book presents a new modeling and simulation tool, applied to social system simulation. The models are coded in the object- and agent-oriented language Bluesss (Blues Simulation System), related to the C++ language. The program code consists of a series of generic declarations of processes. Each of them includes a number of events that are coded in C++. At the runtime, a population of objects is generated. All the objects (agents) start to execute their own events, and interact with one another. During the simulations it is possible to observe the macro-behavior of the population, where some unexpected or "catastrophic" events occur. The examples include a stock market crash, catastrophes in extended prey–predator systems, growing organisms and cancer, epidemics, social inequality and economic decay, mass-service systems, and more. Remarks on possible simultaneous events are also included.

Uncertainty In Geographical Information

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Author : Jingxiong Zhang
language : en
Publisher: CRC Press
Release Date : 2002-03-29

Uncertainty In Geographical Information written by Jingxiong Zhang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-29 with Technology & Engineering categories.

As Geographic Information Systems (GIS) have developed and their applications have been extended, the issue of uncertainty has become increasingly recognized. It is highlighted by the need to demystify the inherently complex geographical world to facilitate computerization in GIS, by the inaccuracies that emerge from man-machine interactions in dat