Dynamics under Uncertainty

Dynamics under Uncertainty

Author: Dragan Pamucar

Publisher: MDPI

Published: 2021-09-08

Total Pages: 210

ISBN-13: 3036515763

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The dynamics of systems have proven to be very powerful tools in understanding the behavior of different natural phenomena throughout the last two centuries. However, the attributes of natural systems are observed to deviate from their classical states due to the effect of different types of uncertainties. Actually, randomness and impreciseness are the two major sources of uncertainties in natural systems. Randomness is modeled by different stochastic processes and impreciseness could be modeled by fuzzy sets, rough sets, Dempster–Shafer theory, etc.


Book Synopsis Dynamics under Uncertainty by : Dragan Pamucar

Download or read book Dynamics under Uncertainty written by Dragan Pamucar and published by MDPI. This book was released on 2021-09-08 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of systems have proven to be very powerful tools in understanding the behavior of different natural phenomena throughout the last two centuries. However, the attributes of natural systems are observed to deviate from their classical states due to the effect of different types of uncertainties. Actually, randomness and impreciseness are the two major sources of uncertainties in natural systems. Randomness is modeled by different stochastic processes and impreciseness could be modeled by fuzzy sets, rough sets, Dempster–Shafer theory, etc.


Dynamics Under Uncertainty: Modeling Simulation and Complexity

Dynamics Under Uncertainty: Modeling Simulation and Complexity

Author: Dragan Pamučar

Publisher:

Published: 2021

Total Pages: 210

ISBN-13: 9783036515755

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The dynamics of systems have proven to be very powerful tools in understanding the behavior of different natural phenomena throughout the last two centuries. However, the attributes of natural systems are observed to deviate from their classical states due to the effect of different types of uncertainties. Actually, randomness and impreciseness are the two major sources of uncertainties in natural systems. Randomness is modeled by different stochastic processes and impreciseness could be modeled by fuzzy sets, rough sets, Dempster-Shafer theory, etc.


Book Synopsis Dynamics Under Uncertainty: Modeling Simulation and Complexity by : Dragan Pamučar

Download or read book Dynamics Under Uncertainty: Modeling Simulation and Complexity written by Dragan Pamučar and published by . This book was released on 2021 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of systems have proven to be very powerful tools in understanding the behavior of different natural phenomena throughout the last two centuries. However, the attributes of natural systems are observed to deviate from their classical states due to the effect of different types of uncertainties. Actually, randomness and impreciseness are the two major sources of uncertainties in natural systems. Randomness is modeled by different stochastic processes and impreciseness could be modeled by fuzzy sets, rough sets, Dempster-Shafer theory, etc.


System Dynamics

System Dynamics

Author: Bilash Kanti Bala

Publisher: Springer

Published: 2016-10-28

Total Pages: 287

ISBN-13: 9811020450

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This book covers the broad spectrum of system dynamics methodologies for the modelling and simulation of complex systems: systems thinking, causal diagrams, systems structure of stock and flow diagrams, parameter estimation and tests for confidence building in system dynamics models. It includes a comprehensive review of model validation and policy design and provides a practical presentation of system dynamics modelling. It also offers numerous worked-out examples and case studies in diverse fields using STELLA and VENSIM. The system dynamics methodologies presented here can be applied to nearly all areas of research and planning, and the simulations provided make the complicated issues more easily understandable. System Dynamics: Modelling and Simulation is an essential system dynamics and systems engineering textbook for undergraduate and graduate courses. It also offers an excellent reference guide for managers in industry and policy planners who wish to use modelling and simulation to manage complex systems more effectively, as well as researchers in the fields of modelling and simulation-based systems thinking.


Book Synopsis System Dynamics by : Bilash Kanti Bala

Download or read book System Dynamics written by Bilash Kanti Bala and published by Springer. This book was released on 2016-10-28 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the broad spectrum of system dynamics methodologies for the modelling and simulation of complex systems: systems thinking, causal diagrams, systems structure of stock and flow diagrams, parameter estimation and tests for confidence building in system dynamics models. It includes a comprehensive review of model validation and policy design and provides a practical presentation of system dynamics modelling. It also offers numerous worked-out examples and case studies in diverse fields using STELLA and VENSIM. The system dynamics methodologies presented here can be applied to nearly all areas of research and planning, and the simulations provided make the complicated issues more easily understandable. System Dynamics: Modelling and Simulation is an essential system dynamics and systems engineering textbook for undergraduate and graduate courses. It also offers an excellent reference guide for managers in industry and policy planners who wish to use modelling and simulation to manage complex systems more effectively, as well as researchers in the fields of modelling and simulation-based systems thinking.


Sub-structure Coupling for Dynamic Analysis

Sub-structure Coupling for Dynamic Analysis

Author: Hector Jensen

Publisher: Springer

Published: 2019-03-26

Total Pages: 231

ISBN-13: 3030128199

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This book combines a model reduction technique with an efficient parametrization scheme for the purpose of solving a class of complex and computationally expensive simulation-based problems involving finite element models. These problems, which have a wide range of important applications in several engineering fields, include reliability analysis, structural dynamic simulation, sensitivity analysis, reliability-based design optimization, Bayesian model validation, uncertainty quantification and propagation, etc. The solution of this type of problems requires a large number of dynamic re-analyses. To cope with this difficulty, a model reduction technique known as substructure coupling for dynamic analysis is considered. While the use of reduced order models alleviates part of the computational effort, their repetitive generation during the simulation processes can be computational expensive due to the substantial computational overhead that arises at the substructure level. In this regard, an efficient finite element model parametrization scheme is considered. When the division of the structural model is guided by such a parametrization scheme, the generation of a small number of reduced order models is sufficient to run the large number of dynamic re-analyses. Thus, a drastic reduction in computational effort is achieved without compromising the accuracy of the results. The capabilities of the developed procedures are demonstrated in a number of simulation-based problems involving uncertainty.


Book Synopsis Sub-structure Coupling for Dynamic Analysis by : Hector Jensen

Download or read book Sub-structure Coupling for Dynamic Analysis written by Hector Jensen and published by Springer. This book was released on 2019-03-26 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines a model reduction technique with an efficient parametrization scheme for the purpose of solving a class of complex and computationally expensive simulation-based problems involving finite element models. These problems, which have a wide range of important applications in several engineering fields, include reliability analysis, structural dynamic simulation, sensitivity analysis, reliability-based design optimization, Bayesian model validation, uncertainty quantification and propagation, etc. The solution of this type of problems requires a large number of dynamic re-analyses. To cope with this difficulty, a model reduction technique known as substructure coupling for dynamic analysis is considered. While the use of reduced order models alleviates part of the computational effort, their repetitive generation during the simulation processes can be computational expensive due to the substantial computational overhead that arises at the substructure level. In this regard, an efficient finite element model parametrization scheme is considered. When the division of the structural model is guided by such a parametrization scheme, the generation of a small number of reduced order models is sufficient to run the large number of dynamic re-analyses. Thus, a drastic reduction in computational effort is achieved without compromising the accuracy of the results. The capabilities of the developed procedures are demonstrated in a number of simulation-based problems involving uncertainty.


Reachable Sets of Dynamic Systems

Reachable Sets of Dynamic Systems

Author: Stanislaw Raczynski

Publisher: Elsevier

Published: 2023-04-21

Total Pages: 216

ISBN-13: 0443133832

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Reachable Sets of Dynamic Systems: Uncertainty, Sensitivity, and Complex Dynamics introduces differential inclusions, providing an overview as well as multiple examples of its interdisciplinary applications. The design of dynamic systems of any type is an important issue as is the influence of uncertainty in model parameters and model sensitivity. The possibility of calculating the reachable sets may be a powerful additional tool in such tasks. This book can help graduate students, researchers, and engineers working in the field of computer simulation and model building, in the calculation of reachable sets of dynamic models. Introduces methodologies and approaches to the modeling and simulation of dynamic systems Presents uncertainty treatment and model sensitivity are described, and interdisciplinary examples Explores applications of differential inclusions in modeling and simulation


Book Synopsis Reachable Sets of Dynamic Systems by : Stanislaw Raczynski

Download or read book Reachable Sets of Dynamic Systems written by Stanislaw Raczynski and published by Elsevier. This book was released on 2023-04-21 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reachable Sets of Dynamic Systems: Uncertainty, Sensitivity, and Complex Dynamics introduces differential inclusions, providing an overview as well as multiple examples of its interdisciplinary applications. The design of dynamic systems of any type is an important issue as is the influence of uncertainty in model parameters and model sensitivity. The possibility of calculating the reachable sets may be a powerful additional tool in such tasks. This book can help graduate students, researchers, and engineers working in the field of computer simulation and model building, in the calculation of reachable sets of dynamic models. Introduces methodologies and approaches to the modeling and simulation of dynamic systems Presents uncertainty treatment and model sensitivity are described, and interdisciplinary examples Explores applications of differential inclusions in modeling and simulation


System Dynamics Fast Guide: A Basic Tutorial with Examples for Modeling, Analysis and Simulate the Complexity of Business and Environmental System

System Dynamics Fast Guide: A Basic Tutorial with Examples for Modeling, Analysis and Simulate the Complexity of Business and Environmental System

Author:

Publisher:

Published: 2018-09-28

Total Pages: 278

ISBN-13: 9781724126535

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System Dynamics finds its main applications in the complex and ill-defined environments. System Dynamics is radically different from other techniques applied to the construction of models of socioeconomic systems, such as econometrics based on a behavioral approach. The basic objective of System Dynamics is to understand the structure that causes the behavior of the system. System Dynamics allows the construction of models after a careful analysis of the elements of the system. This book provides a clear and orderly vision of how to build a simulation model with System Dynamics.The System Dynamics finds its main applications in the complex and ill-defined environments, where the decisions of the human being intervene. The point of view of the System Dynamics is radically different from that of other techniques applied to the construction of models of socioeconomic systems, such as econometrics based on a behavioral approach. The basic objective of System Dynamics is to understand the structural causes that cause the behavior of the system.The System Dynamics allows the construction of models after a careful analysis of the elements of the system. This analysis allows to extract the internal logic of the model, and with it to try an understanding of the long-term evolution of the system.There is an extensive bibliography on System Dynamics, this book provides a clear and orderly vision of how to build a simulation model with this technique. It includes detailed modeling of environmental systems, business, social and physical systems.System DynamicsEnvironmental System Dynamics4.1. Population Growth 4.2. Modeling the Ecology of a Natural Reserve 4.3. Effects of the Intensive Farming 4.4. The Fishery of Shrimp 4.5. Rabbits and Foxes 4.6. A Study of Hogs 4.7. Ingestion of Toxins 4.8. The Barays of Angkor Business Dynamics4.9. Production and Inventory 4.10. CO2 Emissions 4.11. How to work more and better 4.12. Faults 4.13. Project Dynamics 4.14. Innovatory Companies 4.15. Quality Control 4.16. The impact of a Business Plan Social System Dynamics4.17. Filling a Glass 4.18. Dynamics of a Segmented Population 4.19. The Young Ambitious Worker 4.20. Development of an Epidemic 4.21. The Dynamics of Two Clocks Dynamics of Physical Systems4.22. The Tank 4.23. Study of the Oscillatory Movements 4.24. Design of a Chemical Reactor The diverse range of examples provided in this book, will allow readers to:- Build models without deep mathematical knowledge.- Simulate system behaviors and optimize complex systems.- Define strategies avoiding unintended consequences.- Evaluate the effectiveness of its policies.About the authorJuan Martín García is a worldwide recognized expert in System Dynamics, with more than twenty years of experience in this field. Ph.D. Industrial Engineer (Spain) and Postgraduated Diploma in Business Dynamics at Massachusetts Institute of Technology MIT (USA). It teaches Vensim online courses in http://vensim.com/vensim-online-courses/ based on System Dynamics.


Book Synopsis System Dynamics Fast Guide: A Basic Tutorial with Examples for Modeling, Analysis and Simulate the Complexity of Business and Environmental System by :

Download or read book System Dynamics Fast Guide: A Basic Tutorial with Examples for Modeling, Analysis and Simulate the Complexity of Business and Environmental System written by and published by . This book was released on 2018-09-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: System Dynamics finds its main applications in the complex and ill-defined environments. System Dynamics is radically different from other techniques applied to the construction of models of socioeconomic systems, such as econometrics based on a behavioral approach. The basic objective of System Dynamics is to understand the structure that causes the behavior of the system. System Dynamics allows the construction of models after a careful analysis of the elements of the system. This book provides a clear and orderly vision of how to build a simulation model with System Dynamics.The System Dynamics finds its main applications in the complex and ill-defined environments, where the decisions of the human being intervene. The point of view of the System Dynamics is radically different from that of other techniques applied to the construction of models of socioeconomic systems, such as econometrics based on a behavioral approach. The basic objective of System Dynamics is to understand the structural causes that cause the behavior of the system.The System Dynamics allows the construction of models after a careful analysis of the elements of the system. This analysis allows to extract the internal logic of the model, and with it to try an understanding of the long-term evolution of the system.There is an extensive bibliography on System Dynamics, this book provides a clear and orderly vision of how to build a simulation model with this technique. It includes detailed modeling of environmental systems, business, social and physical systems.System DynamicsEnvironmental System Dynamics4.1. Population Growth 4.2. Modeling the Ecology of a Natural Reserve 4.3. Effects of the Intensive Farming 4.4. The Fishery of Shrimp 4.5. Rabbits and Foxes 4.6. A Study of Hogs 4.7. Ingestion of Toxins 4.8. The Barays of Angkor Business Dynamics4.9. Production and Inventory 4.10. CO2 Emissions 4.11. How to work more and better 4.12. Faults 4.13. Project Dynamics 4.14. Innovatory Companies 4.15. Quality Control 4.16. The impact of a Business Plan Social System Dynamics4.17. Filling a Glass 4.18. Dynamics of a Segmented Population 4.19. The Young Ambitious Worker 4.20. Development of an Epidemic 4.21. The Dynamics of Two Clocks Dynamics of Physical Systems4.22. The Tank 4.23. Study of the Oscillatory Movements 4.24. Design of a Chemical Reactor The diverse range of examples provided in this book, will allow readers to:- Build models without deep mathematical knowledge.- Simulate system behaviors and optimize complex systems.- Define strategies avoiding unintended consequences.- Evaluate the effectiveness of its policies.About the authorJuan Martín García is a worldwide recognized expert in System Dynamics, with more than twenty years of experience in this field. Ph.D. Industrial Engineer (Spain) and Postgraduated Diploma in Business Dynamics at Massachusetts Institute of Technology MIT (USA). It teaches Vensim online courses in http://vensim.com/vensim-online-courses/ based on System Dynamics.


Applied Research in Uncertainty Modeling and Analysis

Applied Research in Uncertainty Modeling and Analysis

Author: Bilal M. Ayyub

Publisher: Springer Science & Business Media

Published: 2007-12-29

Total Pages: 547

ISBN-13: 0387235507

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The application areas of uncertainty are numerous and diverse, including all fields of engineering, computer science, systems control and finance. Determining appropriate ways and methods of dealing with uncertainty has been a constant challenge. The theme for this book is better understanding and the application of uncertainty theories. This book, with invited chapters, deals with the uncertainty phenomena in diverse fields. The book is an outgrowth of the Fourth International Symposium on Uncertainty Modeling and Analysis (ISUMA), which was held at the center of Adult Education, College Park, Maryland, in September 2003. All of the chapters have been carefully edited, following a review process in which the editorial committee scrutinized each chapter. The contents of the book are reported in twenty-three chapters, covering more than . . ... pages. This book is divided into six main sections. Part I (Chapters 1-4) presents the philosophical and theoretical foundation of uncertainty, new computational directions in neural networks, and some theoretical foundation of fuzzy systems. Part I1 (Chapters 5-8) reports on biomedical and chemical engineering applications. The sections looks at noise reduction techniques using hidden Markov models, evaluation of biomedical signals using neural networks, and changes in medical image detection using Markov Random Field and Mean Field theory. One of the chapters reports on optimization in chemical engineering processes.


Book Synopsis Applied Research in Uncertainty Modeling and Analysis by : Bilal M. Ayyub

Download or read book Applied Research in Uncertainty Modeling and Analysis written by Bilal M. Ayyub and published by Springer Science & Business Media. This book was released on 2007-12-29 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application areas of uncertainty are numerous and diverse, including all fields of engineering, computer science, systems control and finance. Determining appropriate ways and methods of dealing with uncertainty has been a constant challenge. The theme for this book is better understanding and the application of uncertainty theories. This book, with invited chapters, deals with the uncertainty phenomena in diverse fields. The book is an outgrowth of the Fourth International Symposium on Uncertainty Modeling and Analysis (ISUMA), which was held at the center of Adult Education, College Park, Maryland, in September 2003. All of the chapters have been carefully edited, following a review process in which the editorial committee scrutinized each chapter. The contents of the book are reported in twenty-three chapters, covering more than . . ... pages. This book is divided into six main sections. Part I (Chapters 1-4) presents the philosophical and theoretical foundation of uncertainty, new computational directions in neural networks, and some theoretical foundation of fuzzy systems. Part I1 (Chapters 5-8) reports on biomedical and chemical engineering applications. The sections looks at noise reduction techniques using hidden Markov models, evaluation of biomedical signals using neural networks, and changes in medical image detection using Markov Random Field and Mean Field theory. One of the chapters reports on optimization in chemical engineering processes.


Model Validation and Uncertainty Quantification, Volume 3

Model Validation and Uncertainty Quantification, Volume 3

Author: Robert Barthorpe

Publisher: Springer

Published: 2019-05-30

Total Pages: 299

ISBN-13: 3030120759

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Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics, 2019, the third volume of eight 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: Inverse Problems and Uncertainty Quantification Controlling Uncertainty Validation of Models for Operating Environments Model Validation & Uncertainty Quantification: Decision Making Uncertainty Quantification in Structural Dynamics Uncertainty in Early Stage Design Computational and Uncertainty Quantification Tools


Book Synopsis Model Validation and Uncertainty Quantification, Volume 3 by : Robert Barthorpe

Download or read book Model Validation and Uncertainty Quantification, Volume 3 written by Robert Barthorpe and published by Springer. This book was released on 2019-05-30 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics, 2019, the third volume of eight 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: Inverse Problems and Uncertainty Quantification Controlling Uncertainty Validation of Models for Operating Environments Model Validation & Uncertainty Quantification: Decision Making Uncertainty Quantification in Structural Dynamics Uncertainty in Early Stage Design Computational and Uncertainty Quantification Tools


Simulating Knowledge Dynamics in Innovation Networks

Simulating Knowledge Dynamics in Innovation Networks

Author: Nigel Gilbert

Publisher: Springer

Published: 2014-07-22

Total Pages: 253

ISBN-13: 366243508X

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The competitiveness of firms, regions and countries greatly depends on the generation, dissemination and application of new knowledge. Modern innovation research is challenged by the need to incorporate knowledge generation and dissemination processes into the analysis so as to disentangle the complexity of these dynamic processes. With innovation, however, strong uncertainty, nonlinearities and actor heterogeneity become central factors that are at odds with traditional modeling techniques anchored in equilibrium and homogeneity. This text introduces SKIN (Simulation Knowledge Dynamics in Innovation Networks), an agent-based simulation model that primarily focuses on joint knowledge creation and exchange of knowledge in innovation co‐operations and networks. In this context, knowledge is explicitly modeled and not approximated by, for instance, the level of accumulated R&D investment. The SKIN approach supports applications in different domains ranging from sector-based research activities in knowledge-intensive industries to the activities of international research consortia engaged in basic and applied research. Following a general description of the SKIN model, several applications and modifications are presented. Each chapter introduces in detail the structure of the model, the relevant methodological considerations and the analysis of simulation results, while options for empirically validating the models’ structure and outcomes are also discussed. The book considers the scope of further applications and outlines prospects for the development of joint modeling strategies.


Book Synopsis Simulating Knowledge Dynamics in Innovation Networks by : Nigel Gilbert

Download or read book Simulating Knowledge Dynamics in Innovation Networks written by Nigel Gilbert and published by Springer. This book was released on 2014-07-22 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The competitiveness of firms, regions and countries greatly depends on the generation, dissemination and application of new knowledge. Modern innovation research is challenged by the need to incorporate knowledge generation and dissemination processes into the analysis so as to disentangle the complexity of these dynamic processes. With innovation, however, strong uncertainty, nonlinearities and actor heterogeneity become central factors that are at odds with traditional modeling techniques anchored in equilibrium and homogeneity. This text introduces SKIN (Simulation Knowledge Dynamics in Innovation Networks), an agent-based simulation model that primarily focuses on joint knowledge creation and exchange of knowledge in innovation co‐operations and networks. In this context, knowledge is explicitly modeled and not approximated by, for instance, the level of accumulated R&D investment. The SKIN approach supports applications in different domains ranging from sector-based research activities in knowledge-intensive industries to the activities of international research consortia engaged in basic and applied research. Following a general description of the SKIN model, several applications and modifications are presented. Each chapter introduces in detail the structure of the model, the relevant methodological considerations and the analysis of simulation results, while options for empirically validating the models’ structure and outcomes are also discussed. The book considers the scope of further applications and outlines prospects for the development of joint modeling strategies.


Uncertainty and Sensitivity Analysis in Archaeological Computational Modeling

Uncertainty and Sensitivity Analysis in Archaeological Computational Modeling

Author: Marieka Brouwer Burg

Publisher: Springer

Published: 2016-05-18

Total Pages: 189

ISBN-13: 3319278339

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This volume deals with the pressing issue of uncertainty in archaeological modeling. Detecting where and when uncertainty is introduced to the modeling process is critical, as are strategies for minimizing, reconciling, or accommodating such uncertainty. Included chapters provide unique perspectives on uncertainty in archaeological modeling, ranging in both theoretical and methodological orientation. The strengths and weaknesses of various identification and mitigation techniques are discussed, in particular sensitivity analysis. The chapters demonstrate that for archaeological modeling purposes, there is no quick fix for uncertainty; indeed, each archaeological model requires intensive consideration of uncertainty and specific applications for calibration and validation. As very few such techniques have been problematized in a systematic manner or published in the archaeological literature, this volume aims to provide guidance and direction to other modelers in the field by distilling some basic principles for model testing derived from insight gathered in the case studies presented. Additionally, model applications and their attendant uncertainties are presented from distinct spatio-temporal contexts and will appeal to a broad range of archaeological modelers. This volume will also be of interest to non-modeling archaeologists, as consideration of uncertainty when interpreting the archaeological record is also a vital concern for the development of non-formal (or implicit) models of human behavior in the past.


Book Synopsis Uncertainty and Sensitivity Analysis in Archaeological Computational Modeling by : Marieka Brouwer Burg

Download or read book Uncertainty and Sensitivity Analysis in Archaeological Computational Modeling written by Marieka Brouwer Burg and published by Springer. This book was released on 2016-05-18 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the pressing issue of uncertainty in archaeological modeling. Detecting where and when uncertainty is introduced to the modeling process is critical, as are strategies for minimizing, reconciling, or accommodating such uncertainty. Included chapters provide unique perspectives on uncertainty in archaeological modeling, ranging in both theoretical and methodological orientation. The strengths and weaknesses of various identification and mitigation techniques are discussed, in particular sensitivity analysis. The chapters demonstrate that for archaeological modeling purposes, there is no quick fix for uncertainty; indeed, each archaeological model requires intensive consideration of uncertainty and specific applications for calibration and validation. As very few such techniques have been problematized in a systematic manner or published in the archaeological literature, this volume aims to provide guidance and direction to other modelers in the field by distilling some basic principles for model testing derived from insight gathered in the case studies presented. Additionally, model applications and their attendant uncertainties are presented from distinct spatio-temporal contexts and will appeal to a broad range of archaeological modelers. This volume will also be of interest to non-modeling archaeologists, as consideration of uncertainty when interpreting the archaeological record is also a vital concern for the development of non-formal (or implicit) models of human behavior in the past.