Download or read book Computationally Efficient Kalman Filter Approaches for Fitting Smoothing Splines written by Xiaoxiao Sun and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smoothing spline models have shown to be effective in various fields (e.g., engineering and biomedical sciences) for understanding complex signals from noisy data. As nonparametric models, smoothing spline ANOVA (Analysis Of variance) models do not fix the structure of the regression function, leading to more flexible model estimates (e.g., linear or nonlinear estimates). The functional ANOVA decomposition of the regression function estimates offers interpretable results that describe the relationship between the outcome variable, and the main and interaction effects of different covariates/predictors. However, smoothing spline ANOVA (SS-ANOVA) models suffer from high computational costs, with a computational complexity of ON3 for N observations. Various numerical approaches can address this problem. In this chapter, we focus on the introduction to a state space representation of SS-ANOVA models. The estimation algorithms based on the Kalman filter are implemented within the SS-ANOVA framework using the state space representation, reducing the computational costs significantly.
Download or read book Curve and Surface Fitting with Splines written by Paul Dierckx and published by Oxford University Press. This book was released on 1995 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many examples, academic as well as taken from real life.
Download or read book Smoothing Splines written by Yuedong Wang and published by CRC Press. This book was released on 2011-06-22 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general class of powerful and flexible modeling techniques, spline smoothing has attracted a great deal of research attention in recent years and has been widely used in many application areas, from medicine to economics. Smoothing Splines: Methods and Applications covers basic smoothing spline models, including polynomial, periodic, spherical, t
Download or read book Kalman Filtering written by Mohinder S. Grewal and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with a solid introduction to the theoretical and practical aspects of Kalman filtering. It has been updated with the latest developments in the implementation and application of Kalman filtering, including adaptations for nonlinear filtering, more robust smoothing methods, and developing applications in navigation. All software is provided in MATLAB, giving readers the opportunity to discover how the Kalman filter works in action and to consider the practical arithmetic needed to preserve the accuracy of results. Note: CD-ROM/DVD and other supplementary materials are not included as part of eBook file. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department -- to obtain the manual, send an email to [email protected].
Download or read book Restricted Kalman Filtering written by Adrian Pizzinga and published by Springer Science & Business Media. This book was released on 2012-07-25 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: In statistics, the Kalman filter is a mathematical method whose purpose is to use a series of measurements observed over time, containing random variations and other inaccuracies, and produce estimates that tend to be closer to the true unknown values than those that would be based on a single measurement alone. This Brief offers developments on Kalman filtering subject to general linear constraints. There are essentially three types of contributions: new proofs for results already established; new results within the subject; and applications in investment analysis and macroeconomics, where the proposed methods are illustrated and evaluated. The Brief has a short chapter on linear state space models and the Kalman filter, aiming to make the book self-contained and to give a quick reference to the reader (notation and terminology). The prerequisites would be a contact with time series analysis in the level of Hamilton (1994) or Brockwell & Davis (2002) and also with linear state models and the Kalman filter – each of these books has a chapter entirely dedicated to the subject. The book is intended for graduate students, researchers and practitioners in statistics (specifically: time series analysis and econometrics).
Download or read book Time Series Analysis by State Space Methods written by James Durbin and published by Oxford University Press. This book was released on 2012-05-03 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive treatment of the state space approach to time series analysis. A distinguishing feature of state space time series models is that observations are regarded as made up of distinct components, which are each modelled separately.
Download or read book Smoothing and Regression written by Michael G. Schimek and published by John Wiley & Sons. This book was released on 2013-05-29 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to a wide variety of univariate and multivariate smoothing techniques for regression Smoothing and Regression: Approaches, Computation, and Application bridges the many gaps that exist among competing univariate and multivariate smoothing techniques. It introduces, describes, and in some cases compares a large number of the latest and most advanced techniques for regression modeling. Unlike many other volumes on this topic, which are highly technical and specialized, this book discusses all methods in light of both computational efficiency and their applicability for real data analysis. Using examples of applications from the biosciences, environmental sciences, engineering, and economics, as well as medical research and marketing, this volume addresses the theory, computation, and application of each approach. A number of the techniques discussed, such as smoothing under shape restrictions or of dependent data, are presented for the first time in book form. Special features of this book include: * Comprehensive coverage of smoothing and regression with software hints and applications from a wide variety of disciplines * A unified, easy-to-follow format * Contributions from more than 25 leading researchers from around the world * More than 150 illustrations also covering new graphical techniques important for exploratory data analysis and visualization of high-dimensional problems * Extensive end-of-chapter references For professionals and aspiring professionals in statistics, applied mathematics, computer science, and econometrics, as well as for researchers in the applied and social sciences, Smoothing and Regression is a unique and important new resource destined to become one the most frequently consulted references in the field.
Download or read book Network Bioscience 2nd Edition written by Marco Pellegrini and published by Frontiers Media SA. This book was released on 2020-03-27 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Network science has accelerated a deep and successful trend in research that influences a range of disciplines like mathematics, graph theory, physics, statistics, data science and computer science (just to name a few) and adapts the relevant techniques and insights to address relevant but disparate social, biological, technological questions. We are now in an era of 'big biological data' supported by cost-effective high-throughput genomic, transcriptomic, proteomic, metabolomic data collection techniques that allow one to take snapshots of the cells' molecular profiles in a systematic fashion. Moreover recently, also phenotypic data, data on diseases, symptoms, patients, etc. are being collected at nation-wide level thus giving us another source of highly related (causal) 'big data'. This wealth of data is usually modeled as networks (aka binary relations, graphs or webs) of interactions, (including protein-protein, metabolic, signaling and transcription-regulatory interactions). The network model is a key view point leading to the uncovering of mesoscale phenomena, thus providing an essential bridge between the observable phenotypes and 'omics' underlying mechanisms. Moreover, network analysis is a powerful 'hypothesis generation' tool guiding the scientific cycle of 'data gathering', 'data interpretation, 'hypothesis generation' and 'hypothesis testing'. A major challenge in contemporary research is the synthesis of deep insights coming from network science with the wealth of data (often noisy, contradictory, incomplete and difficult to replicate) so to answer meaningful biological questions, in a quantifiable way using static and dynamic properties of biological networks.
Download or read book Elements of Statistical Computing written by R.A. Thisted and published by Routledge. This book was released on 2017-10-19 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistics and computing share many close relationships. Computing now permeates every aspect of statistics, from pure description to the development of statistical theory. At the same time, the computational methods used in statistical work span much of computer science. Elements of Statistical Computing covers the broad usage of computing in statistics. It provides a comprehensive account of the most important computational statistics. Included are discussions of numerical analysis, numerical integration, and smoothing. The author give special attention to floating point standards and numerical analysis; iterative methods for both linear and nonlinear equation, such as Gauss-Seidel method and successive over-relaxation; and computational methods for missing data, such as the EM algorithm. Also covered are new areas of interest, such as the Kalman filter, projection-pursuit methods, density estimation, and other computer-intensive techniques.
Download or read book A New Algorithm for Spline Smoothing Based on Smoothing a Stochastic Process written by Robert Kohn and published by . This book was released on 1985 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction and Implementations of the Kalman Filter written by Felix Govaers and published by BoD – Books on Demand. This book was released on 2019-05-22 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sensor data fusion is the process of combining error-prone, heterogeneous, incomplete, and ambiguous data to gather a higher level of situational awareness. In principle, all living creatures are fusing information from their complementary senses to coordinate their actions and to detect and localize danger. In sensor data fusion, this process is transferred to electronic systems, which rely on some "awareness" of what is happening in certain areas of interest. By means of probability theory and statistics, it is possible to model the relationship between the state space and the sensor data. The number of ingredients of the resulting Kalman filter is limited, but its applications are not.
Download or read book Statistics and Physical Oceanography written by National Research Council (U.S.). Committee on Applied and Theoretical Statistics. Panel on Statistics and Oceanography and published by National Academies. This book was released on 1993 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Current Index to Statistics Applications Methods and Theory written by and published by . This book was released on 1998 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
Download or read book Journal of the American Statistical Association written by and published by . This book was released on 2005 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proximal Soil Sensing written by Raphael A. Viscarra Rossel and published by Springer Science & Business Media. This book was released on 2010-07-25 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports on developments in Proximal Soil Sensing (PSS) and high resolution digital soil mapping. PSS has become a multidisciplinary area of study that aims to develop field-based techniques for collecting information on the soil from close by, or within, the soil. Amongst others, PSS involves the use of optical, geophysical, electrochemical, mathematical and statistical methods. This volume, suitable for undergraduate course material and postgraduate research, brings together ideas and examples from those developing and using proximal sensors and high resolution digital soil maps for applications such as precision agriculture, soil contamination, archaeology, peri-urban design and high land-value applications, where there is a particular need for high spatial resolution information. The book in particular covers soil sensor sampling, proximal soil sensor development and use, sensor calibrations, prediction methods for large data sets, applications of proximal soil sensing, and high-resolution digital soil mapping. Key themes: soil sensor sampling – soil sensor calibrations – spatial prediction methods – reflectance spectroscopy – electromagnetic induction and electrical resistivity – radar and gamma radiometrics – multi-sensor platforms – high resolution digital soil mapping - applications Raphael A. Viscarra Rossel is a scientist at the Commonwealth Scientific and Industrial Research Organisation (CSIRO) of Australia. Alex McBratney is Pro-Dean and Professor of Soil Science in the Faculty of Agriculture Food & Natural Resources at the University of Sydney in Australia. Budiman Minasny is a Senior Research Fellow in the Faculty of Agriculture Food & Natural Resources at the University of Sydney in Australia.
Download or read book Proceedings of the 14th International Modal Analysis Conference written by and published by . This book was released on 1996 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Journal of Geomagnetism and Geoelectricity written by and published by . This book was released on 1991 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt:
