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Stochastic control plays an important role in many scientific and applied disciplines including communications, engineering, medicine, finance and many others. It is one of the effective methods being used to find optimal decision-making strategies in applications. The book provides a collection of outstanding investigations in various aspects of stochastic systems and their behavior. The book provides a self-contained treatment on practical aspects of stochastic modeling and calculus including applications drawn from engineering, statistics, and computer science. Readers should be familiar with basic probability theory and have a working knowledge of stochastic calculus. PhD students and researchers in stochastic control will find this book useful.
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L’historien ne travaille que sur des choses douteuses, incertaines, il ne peut en tirer que des conclusions « probables ». Qu’est-ce que le probabilisme en histoire? Quelle est l’importance du jeu du probable? Comment constater nos ignorances? Comment, avec l’âge, l’expérience renonce-t-on aux explications « certaines » et glisse-t-on à un certain probabilisme ? Autant de questions auxquelles dans ces vingt-quatre leçons Guy Thuillier tente d’apporter des réponses. Le probabilisme n’est pas un corps de doctrine, comme le souligne François Monnier dans sa préface, mais une expérience personnelle, chacun doit la mener pour son compte, et inventer ses méthodes pour mettre en doute ses idées, suspendre son jugement. L’historien est condamné à vivre dans le doute, l’incertitude, l’inquiétude ; rien n’est stable, tout est provisoire.
Historiography --- History --- Probability measures --- Measures, Normalized --- Measures, Probability --- Normalized measures --- Distribution (Probability theory) --- History, Modern --- Historical criticism --- Authorship --- Philosophy --- Criticism --- #A0307H --- History as a science --- Historiography. --- Probability measures. --- Philosophy. --- historien --- probabilisme --- obsolescence --- archive --- érudition --- histoire monétaire --- science administrative
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This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.
Distribution (Probability theory. --- Geometry. --- Probability Theory and Stochastic Processes. --- Discrete Mathematics. --- Mathematical Physics. --- Mathematics --- Euclid's Elements --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Discrete mathematics. --- Mathematical physics. --- Physical mathematics --- Physics --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Discrete mathematics --- Geometry --- Mathematical physics
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A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines.
Computer assisted instruction --- Stochastic processes --- Gaussian processes --- Machine learning --- Data processing --- Mathematical models --- 681.3*I26 --- Learning: analogies; concept learning; induction; knowledge acquisition; language acquisition; parameter learning (Artificial intelligence)--See also {681.3*K32} --- Data processing. --- Mathematical models. --- 681.3*I26 Learning: analogies; concept learning; induction; knowledge acquisition; language acquisition; parameter learning (Artificial intelligence)--See also {681.3*K32} --- Learning, Machine --- Artificial intelligence --- Machine theory --- Distribution (Probability theory) --- machine learning --- statistiek --- Bayesian statistics --- Gauss, Carl Friedrich --- Aprenentatge automàtic --- Processos gaussians --- Models matemàtics --- Informàtica --- Distribució (Teoria de la probabilitat) --- Processos estocàstics --- Intel·ligència artificial --- Màquines, Teoria de --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Gaussian processes - Data processing --- Machine learning - Mathematical models
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This book presents a multidisciplinary perspective on chance, with contributions from distinguished researchers in the areas of biology, cognitive neuroscience, economics, genetics, general history, law, linguistics, logic, mathematical physics, statistics, theology and philosophy. The individual chapters are bound together by a general introduction followed by an opening chapter that surveys 2500 years of linguistic, philosophical, and scientific reflections on chance, coincidence, fortune, randomness, luck and related concepts. A main conclusion that can be drawn is that, even after all this time, we still cannot be sure whether chance is a truly fundamental and irreducible phenomenon, in that certain events are simply uncaused and could have been otherwise, or whether it is always simply a reflection of our ignorance. Other challenges that emerge from this book include a better understanding of the contextuality and perspectival character of chance (including its scale-dependence), and the curious fact that, throughout history (including contemporary science), chance has been used both as an explanation and as a hallmark of the absence of explanation. As such, this book challenges the reader to think about chance in a new way and to come to grips with this endlessly fascinating phenomenon.
Philosophy. --- Human genetics. --- Epistemology. --- Philosophy and science. --- Probabilities. --- Physics. --- Cognitive psychology. --- Philosophy of Science. --- History and Philosophical Foundations of Physics. --- Probability Theory and Stochastic Processes. --- Cognitive Psychology. --- Human Genetics. --- Natural philosophy --- Philosophy, Natural --- Probability --- Statistical inference --- Science and philosophy --- Epistemology --- Theory of knowledge --- Mental philosophy --- Psychology, Cognitive --- Physical sciences --- Dynamics --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Science --- Philosophy --- Psychology --- Genetics --- Heredity, Human --- Human biology --- Physical anthropology --- Humanities --- Cognitive science --- Genetic epistemology. --- Distribution (Probability theory. --- Consciousness. --- Apperception --- Mind and body --- Perception --- Spirit --- Self --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Developmental psychology --- Knowledge, Theory of --- Normal science --- Philosophy of science
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This book is open access under a CC BY 4.0 license. This book addresses the physical phenomenon of events that seem to occur spontaneously and without any known cause. These are to be contrasted with events that happen in a (pre-)determined, predictable, lawful, and causal way. All our knowledge is based on self-reflexive theorizing, as well as on operational means of empirical perception. Some of the questions that arise are the following: are these limitations reflected by our models? Under what circumstances does chance kick in? Is chance in physics merely epistemic? In other words, do we simply not know enough, or use too crude levels of description for our predictions? Or are certain events "truly", that is, irreducibly, random? The book tries to answer some of these questions by introducing intrinsic, embedded observers and provable unknowns; that is, observables and procedures which are certified (relative to the assumptions) to be unknowable or undoable. A (somewhat iconoclastic) review of quantum mechanics is presented which is inspired by quantum logic. Postulated quantum (un-)knowables are reviewed. More exotic unknowns originate in the assumption of classical continua, and in finite automata and generalized urn models, which mimic complementarity and yet maintain value definiteness. Traditional conceptions of free will, miracles and dualistic interfaces are based on gaps in an otherwise deterministic universe. .
Physics. --- Epistemology. --- Philosophy and science. --- Probabilities. --- History and Philosophical Foundations of Physics. --- Theoretical, Mathematical and Computational Physics. --- Probability Theory and Stochastic Processes. --- Philosophy of Science. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Science and philosophy --- Science --- Epistemology --- Theory of knowledge --- Philosophy --- Psychology --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Genetic epistemology. --- Distribution (Probability theory. --- Philosophy. --- Normal science --- Philosophy of science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Developmental psychology --- Knowledge, Theory of --- Mathematical physics. --- Physical mathematics --- Physics --- Self-reflexive knowledge --- Physical chaos --- Physical random number generators --- Irreducible randomness --- Randomness in physics --- Physical indeterminism --- Acausality in physics --- Ecotoxicology. --- Environmental management. --- Waste management. --- Environmental Management. --- Waste Management/Waste Technology.
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These Proceedings offer a selection of peer-reviewed research and survey papers by some of the foremost international researchers in the fields of finance, energy, stochastics and risk, who present their latest findings on topical problems. The papers cover the areas of stochastic modeling in energy and financial markets; risk management with environmental factors from a stochastic control perspective; and valuation and hedging of derivatives in markets dominated by renewables, all of which further develop the theory of stochastic analysis and mathematical finance. The papers were presented at the first conference on “Stochastics of Environmental and Financial Economics (SEFE)”, being part of the activity in the SEFE research group of the Centre of Advanced Study (CAS) at the Academy of Sciences in Oslo, Norway during the 2014/2015 academic year.
Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Mathematics. --- Partial differential equations. --- Game theory. --- System theory. --- Calculus of variations. --- Probabilities. --- Environmental economics. --- Systems Theory, Control. --- Probability Theory and Stochastic Processes. --- Environmental Economics. --- Game Theory, Economics, Social and Behav. Sciences. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Economics --- Environmental quality --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Systems, Theory of --- Systems science --- Science --- Games, Theory of --- Theory of games --- Mathematical models --- Partial differential equations --- Math --- Environmental aspects --- Economic aspects --- Philosophy --- Distribution (Probability theory. --- Differential equations, partial. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Systems theory. --- Systems Theory --- Control
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This book demonstrates how nonlinear/non-Gaussian Bayesian time series estimation methods were used to produce a probability distribution of potential MH370 flight paths. It provides details of how the probabilistic models of aircraft flight dynamics, satellite communication system measurements, environmental effects and radar data were constructed and calibrated. The probability distribution was used to define the search zone in the southern Indian Ocean. The book describes particle-filter based numerical calculation of the aircraft flight-path probability distribution and validates the method using data from several of the involved aircraft’s previous flights. Finally it is shown how the Reunion Island flaperon debris find affects the search probability distribution.
Engineering. --- Mathematical statistics. --- Probabilities. --- Statistics. --- Signal, Image and Speech Processing. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Probability Theory and Stochastic Processes. --- Probability and Statistics in Computer Science. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Probability --- Statistical inference --- Mathematics --- Statistics, Mathematical --- Construction --- Econometrics --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Statistics --- Probabilities --- Sampling (Statistics) --- Industrial arts --- Technology --- Distribution (Probability theory. --- Computer science. --- Informatics --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Signal processing. --- Image processing. --- Speech processing systems. --- Statistics . --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication)
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This open access book focuses on both the theory and practice associated with the tools and approaches for decisionmaking in the face of deep uncertainty. It explores approaches and tools supporting the design of strategic plans under deep uncertainty, and their testing in the real world, including barriers and enablers for their use in practice. The book broadens traditional approaches and tools to include the analysis of actors and networks related to the problem at hand. It also shows how lessons learned in the application process can be used to improve the approaches and tools used in the design process. The book offers guidance in identifying and applying appropriate approaches and tools to design plans, as well as advice on implementing these plans in the real world. For decisionmakers and practitioners, the book includes realistic examples and practical guidelines that should help them understand what decisionmaking under deep uncertainty is and how it may be of assistance to them. Decision Making under Deep Uncertainty: From Theory to Practice is divided into four parts. Part I presents five approaches for designing strategic plans under deep uncertainty: Robust Decision Making, Dynamic Adaptive Planning, Dynamic Adaptive Policy Pathways, Info-Gap Decision Theory, and Engineering Options Analysis. Each approach is worked out in terms of its theoretical foundations, methodological steps to follow when using the approach, latest methodological insights, and challenges for improvement. In Part II, applications of each of these approaches are presented. Based on recent case studies, the practical implications of applying each approach are discussed in depth. Part III focuses on using the approaches and tools in real-world contexts, based on insights from real-world cases. Part IV contains conclusions and a synthesis of the lessons that can be drawn for designing, applying, and implementing strategic plans under deep uncertainty, as well as recommendations for future work. The publication of this book has been funded by the Radboud University, the RAND Corporation, Delft University of Technology, and Deltares.
Operations research. --- Differentiable dynamical systems. --- Distribution (Probability theory. --- Operations Research/Decision Theory. --- Dynamical Systems and Ergodic Theory. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Decision making. --- Dynamics. --- Ergodic theory. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Decision making --- Business --- Operations research --- Dynamics --- Ergodic theory
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This book covers seismic probabilistic risk assessment (S-PRA) and related studies which have become more important to increase the safety of nuclear facilities against earthquakes and tsunamis in the face of the many uncertainties after the Fukushima accident. The topics are (1) Active faults and active tectonics important for seismic hazard assessment of nuclear facilities,(2) Seismic source modeling and simulation and modeling techniques indispensable for strong ground motion prediction, and (3) PRA with external hazard and risk communication. The Fukushima accident has showed us the limitations of the deterministic evaluation approach to external events (an earthquake and tsunami) in which there are many uncertainties. Furthermore, public anxiety regarding nuclear safety because of an unexpected threat caused by an earthquake or tsunami is growing. The current policy on the estimation of the design basis of ground motion as well as tsunami height still has not been improved following the Fukushima accident. In particular, the risk concept in a nuclear system regarding seismic motion and a tsunami beyond the design basis is indispensable. Therefore, research and development for PRA enhancing nuclear safety are being actively pursued not only in Japan but also worldwide. This book provides an opportunity for readers to consider the future direction of nuclear safety vis-à-vis natural disasters.
Environmental Sciences --- Earth & Environmental Sciences --- Environment. --- Nuclear energy. --- Natural disasters. --- Probabilities. --- Quality control. --- Reliability. --- Industrial safety. --- Environmental management. --- Environmental Management. --- Nuclear Energy. --- Natural Hazards. --- Quality Control, Reliability, Safety and Risk. --- Probability Theory and Stochastic Processes. --- Environmental stewardship --- Stewardship, Environmental --- Environmental sciences --- Management --- Industrial accidents --- Industries --- Job safety --- Occupational hazards, Prevention of --- Occupational health and safety --- Occupational safety and health --- Prevention of industrial accidents --- Prevention of occupational hazards --- Safety, Industrial --- Safety engineering --- Safety measures --- Safety of workers --- Accidents --- System safety --- Dependability --- Trustworthiness --- Conduct of life --- Factory management --- Industrial engineering --- Reliability (Engineering) --- Sampling (Statistics) --- Standardization --- Quality assurance --- Quality of products --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Natural calamities --- Disasters --- Atomic energy --- Atomic power --- Energy, Atomic --- Energy, Nuclear --- Nuclear power --- Power, Atomic --- Power, Nuclear --- Force and energy --- Nuclear physics --- Power resources --- Nuclear engineering --- Nuclear facilities --- Nuclear power plants --- Prevention --- Geology. --- System safety. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Safety, System --- Safety of systems --- Systems safety --- Industrial safety --- Systems engineering --- Geognosy --- Geoscience --- Earth sciences --- Natural history --- Environmental Management
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