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| Author | : Sebastian Reich |
| Publisher | : Cambridge University Press |
| Total Pages | : 308 |
| Release | : 2015-05-14 |
| Genre | : Computers |
| ISBN | : 1107069394 |
This book covers key ideas and concepts. It is an ideal introduction for graduate students in any field where Bayesian data assimilation is applied.
| Author | : Source Wikipedia |
| Publisher | : University-Press.org |
| Total Pages | : 30 |
| Release | : 2013-09 |
| Genre | : |
| ISBN | : 9781230488592 |
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 28. Chapters: Bayesian inference, Calculating demand forecast accuracy, Consensus forecast, Data assimilation, Demand forecasting, Ensemble forecasting, Fan chart (time series), Forecast bias, Forecast skill, Futures techniques, Growth curve, Hindcast, International Futures, Meteorological reanalysis, Mixed data sampling, Political forecasting, Probabilistic forecasting, Probability of precipitation, Tolerance interval, Trend estimation. Excerpt: In statistics, Bayesian inference is a method of inference in which Bayes' rule is used to update the probability estimate for a hypothesis as additional evidence is learned. Bayesian updating is an important technique throughout statistics, and especially in mathematical statistics. For some cases, exhibiting a Bayesian derivation for a statistical method automatically ensures that the method works as well as any competing method. Bayesian updating is especially important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a range of fields including science, engineering, philosophy, medicine, and law. In the philosophy of decision theory, Bayesian inference is closely related to discussions of subjective probability, often called "Bayesian probability." Bayesian probability provides a rational method for updating beliefs; however, non-Bayesian updating rules are compatible with rationality, according to philosophers Ian Hacking and Bas van Fraassen. Bayesian inference derives the posterior probability as a consequence of two antecedents, a prior probability and a "likelihood function" derived from a probability model for the data to be observed. Bayesian inference computes the posterior probability according to Bayes' rule: where Note that what affects the value of for different values of is only the factors and, which both appear in the...
| Author | : Huan Wu |
| Publisher | : John Wiley & Sons |
| Total Pages | : 352 |
| Release | : 2021-08-10 |
| Genre | : Science |
| ISBN | : 1119427215 |
Recent advances in the modeling and remote sensing of droughts and floods Droughts and floods are causing increasing damage worldwide, often with devastating short- and long-term impacts on human society. Forecasting when they will occur, monitoring them as they develop, and learning from the past to improve disaster management is vital. Global Drought and Flood: Observation, Modeling, and Prediction presents recent advances in the modeling and remote sensing of droughts and floods. It also describes the techniques and products currently available and how they are being used in practice. Volume highlights include: Remote sensing approaches for mapping droughts and floods Physical and statistical models for monitoring and forecasting hydrologic hazards Features of various drought and flood systems and products Use by governments, humanitarian, and development stakeholders in recent disaster cases Improving the collaboration between hazard information provision and end users The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals.
| Author | : Andy Pole |
| Publisher | : CRC Press |
| Total Pages | : 432 |
| Release | : 2018-10-08 |
| Genre | : Business & Economics |
| ISBN | : 1482267438 |
Practical in its approach, Applied Bayesian Forecasting and Time Series Analysis provides the theories, methods, and tools necessary for forecasting and the analysis of time series. The authors unify the concepts, model forms, and modeling requirements within the framework of the dynamic linear mode (DLM). They include a complete theoretical development of the DLM and illustrate each step with analysis of time series data. Using real data sets the authors: Explore diverse aspects of time series, including how to identify, structure, explain observed behavior, model structures and behaviors, and interpret analyses to make informed forecasts Illustrate concepts such as component decomposition, fundamental model forms including trends and cycles, and practical modeling requirements for routine change and unusual events Conduct all analyses in the BATS computer programs, furnishing online that program and the more than 50 data sets used in the text The result is a clear presentation of the Bayesian paradigm: quantified subjective judgements derived from selected models applied to time series observations. Accessible to undergraduates, this unique volume also offers complete guidelines valuable to researchers, practitioners, and advanced students in statistics, operations research, and engineering.
| Author | : Kody Law |
| Publisher | : Springer |
| Total Pages | : 256 |
| Release | : 2015-09-05 |
| Genre | : Mathematics |
| ISBN | : 3319203258 |
This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters. This book is aimed at mathematical researchers interested in a systematic development of this interdisciplinary field, and at researchers from the geosciences, and a variety of other scientific fields, who use tools from data assimilation to combine data with time-dependent models. The numerous examples and illustrations make understanding of the theoretical underpinnings of data assimilation accessible. Furthermore, the examples, exercises and MATLAB software, make the book suitable for students in applied mathematics, either through a lecture course, or through self-study.
| Author | : Daniel Sanz-Alonso |
| Publisher | : Cambridge University Press |
| Total Pages | : 227 |
| Release | : 2023-08-10 |
| Genre | : Computers |
| ISBN | : 1009414321 |
A clear and concise mathematical introduction to the subjects of inverse problems and data assimilation, and their inter-relations.
| Author | : Peter Jan Van Leeuwen |
| Publisher | : Springer |
| Total Pages | : 130 |
| Release | : 2015-07-22 |
| Genre | : Mathematics |
| ISBN | : 3319183478 |
This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.
| Author | : Mark Asch |
| Publisher | : SIAM |
| Total Pages | : 310 |
| Release | : 2016-12-29 |
| Genre | : Mathematics |
| ISBN | : 1611974542 |
Data assimilation is an approach that combines observations and model output, with the objective of improving the latter. This book places data assimilation into the broader context of inverse problems and the theory, methods, and algorithms that are used for their solution. It provides a framework for, and insight into, the inverse problem nature of data assimilation, emphasizing why and not just how. Methods and diagnostics are emphasized, enabling readers to readily apply them to their own field of study. Readers will find a comprehensive guide that is accessible to nonexperts; numerous examples and diverse applications from a broad range of domains, including geophysics and geophysical flows, environmental acoustics, medical imaging, mechanical and biomedical engineering, economics and finance, and traffic control and urban planning; and the latest methods for advanced data assimilation, combining variational and statistical approaches.
| Author | : Mike West |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 720 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475793650 |
In this book we are concerned with Bayesian learning and forecast ing in dynamic environments. We describe the structure and theory of classes of dynamic models, and their uses in Bayesian forecasting. The principles, models and methods of Bayesian forecasting have been developed extensively during the last twenty years. This devel opment has involved thorough investigation of mathematical and sta tistical aspects of forecasting models and related techniques. With this has come experience with application in a variety of areas in commercial and industrial, scientific and socio-economic fields. In deed much of the technical development has been driven by the needs of forecasting practitioners. As a result, there now exists a relatively complete statistical and mathematical framework, although much of this is either not properly documented or not easily accessible. Our primary goals in writing this book have been to present our view of this approach to modelling and forecasting, and to provide a rea sonably complete text for advanced university students and research workers. The text is primarily intended for advanced undergraduate and postgraduate students in statistics and mathematics. In line with this objective we present thorough discussion of mathematical and statistical features of Bayesian analyses of dynamic models, with illustrations, examples and exercises in each Chapter.
| Author | : Henry D. I. Abarbanel |
| Publisher | : Cambridge University Press |
| Total Pages | : 208 |
| Release | : 2022-02-17 |
| Genre | : Science |
| ISBN | : 1009021702 |
Data assimilation is a hugely important mathematical technique, relevant in fields as diverse as geophysics, data science, and neuroscience. This modern book provides an authoritative treatment of the field as it relates to several scientific disciplines, with a particular emphasis on recent developments from machine learning and its role in the optimisation of data assimilation. Underlying theory from statistical physics, such as path integrals and Monte Carlo methods, are developed in the text as a basis for data assimilation, and the author then explores examples from current multidisciplinary research such as the modelling of shallow water systems, ocean dynamics, and neuronal dynamics in the avian brain. The theory of data assimilation and machine learning is introduced in an accessible and unified manner, and the book is suitable for undergraduate and graduate students from science and engineering without specialized experience of statistical physics.
