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Author: STANFORD UNIV CA DEPT OF STATISTICS. Publisher: ISBN: Category : Bayesian statistical decision Languages : en Pages : 50
Book Description
A smoothness priors approach to transfer function estimation from stationary time series is shown. An infinite order impulse response model plus an infinite order additive AR noise model is assumed. This is algebraically equivalent to an infinite order ARMAX plus white noise model. A finite order ARMAX model approximation to this model is actually fitted to data. Frequency domain smoothness priors are assumed on the ARMAX polynomials and smoothness hyperparameters balance the tradeoff between the infidelity of the model to the data and the infidelity of the model to the smoothness constraints. The likelihood of the hyperparameters is maximized by a least squares gradient search computational procedure. The method is illustrated by the analysis of the Box-Jenkins series J data. Some of the statistical properties of the method are explored in Monte-Carlo simulation studies. Keywords: Bayesian model, Smoothness priors, Time series analysis, Transfer function estimation.
Author: STANFORD UNIV CA DEPT OF STATISTICS. Publisher: ISBN: Category : Bayesian statistical decision Languages : en Pages : 50
Book Description
A smoothness priors approach to transfer function estimation from stationary time series is shown. An infinite order impulse response model plus an infinite order additive AR noise model is assumed. This is algebraically equivalent to an infinite order ARMAX plus white noise model. A finite order ARMAX model approximation to this model is actually fitted to data. Frequency domain smoothness priors are assumed on the ARMAX polynomials and smoothness hyperparameters balance the tradeoff between the infidelity of the model to the data and the infidelity of the model to the smoothness constraints. The likelihood of the hyperparameters is maximized by a least squares gradient search computational procedure. The method is illustrated by the analysis of the Box-Jenkins series J data. Some of the statistical properties of the method are explored in Monte-Carlo simulation studies. Keywords: Bayesian model, Smoothness priors, Time series analysis, Transfer function estimation.
Author: Genshiro Kitagawa Publisher: Springer Science & Business Media ISBN: 1461207614 Category : Mathematics Languages : en Pages : 265
Book Description
Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression "smoothness priors" state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian model and the use of likelihood as a measure of the goodness of fit of the model. The emphasis is on a general state space approach in which the recursive conditional distributions for prediction, filtering, and smoothing are realized using a variety of nonstandard methods including numerical integration, a Gaussian mixture distribution-two filter smoothing formula, and a Monte Carlo "particle-path tracing" method in which the distributions are approximated by many realizations. The methods are applicable for modeling time series with complex structures.
Author: David Brillinger Publisher: Springer Science & Business Media ISBN: 1461392969 Category : Mathematics Languages : en Pages : 391
Book Description
This IMA Volume in Mathematics and its Applications NEW DIRECTIONS IN TIME SERIES ANALYSIS, PART II is based on the proceedings of the IMA summer program "New Directions in Time Series Analysis. " We are grateful to David Brillinger, Peter Caines, John Geweke, Emanuel Parzen, Murray Rosenblatt, and Murad Taqqu for organizing the program and we hope that the remarkable excitement and enthusiasm of the participants in this interdisciplinary effort are communicated to the reader. A vner Friedman Willard Miller, Jr. PREFACE Time Series Analysis is truly an interdisciplinary field because development of its theory and methods requires interaction between the diverse disciplines in which it is applied. To harness its great potential, strong interaction must be encouraged among the diverse community of statisticians and other scientists whose research involves the analysis of time series data. This was the goal of the IMA Workshop on "New Directions in Time Series Analysis. " The workshop was held July 2-July 27, 1990 and was organized by a committee consisting of Emanuel Parzen (chair), David Brillinger, Murray Rosenblatt, Murad S. Taqqu, John Geweke, and Peter Caines. Constant guidance and encouragement was provided by Avner Friedman, Director of the IMA, and his very helpful and efficient staff. The workshops were organized by weeks. It may be of interest to record the themes that were announced in the IMA newsletter describing the workshop: l.
Author: Helcio R.B. Orlande Publisher: CRC Press ISBN: 1000362450 Category : Science Languages : en Pages : 299
Book Description
This book introduces the fundamental concepts of inverse heat transfer solutions and their applications for solving problems in convective, conductive, radiative, and multi-physics problems. Inverse Heat Transfer: Fundamentals and Applications, Second Edition includes techniques within the Bayesian framework of statistics for the solution of inverse problems. By modernizing the classic work of the late Professor M. Necati Özisik and adding new examples and problems, this new edition provides a powerful tool for instructors, researchers, and graduate students studying thermal-fluid systems and heat transfer. FEATURES Introduces the fundamental concepts of inverse heat transfer Presents in systematic fashion the basic steps of powerful inverse solution techniques Develops inverse techniques of parameter estimation, function estimation, and state estimation Applies these inverse techniques to the solution of practical inverse heat transfer problems Shows inverse techniques for conduction, convection, radiation, and multi-physics phenomena M. Necati Özisik (1923–2008) retired in 1998 as Professor Emeritus of North Carolina State University’s Mechanical and Aerospace Engineering Department. Helcio R. B. Orlande is a Professor of Mechanical Engineering at the Federal University of Rio de Janeiro (UFRJ), where he was the Department Head from 2006 to 2007.
Author: Steven Brown Publisher: Elsevier ISBN: 0444641661 Category : Science Languages : en Pages : 2948
Book Description
Comprehensive Chemometrics, Second Edition, Four Volume Set features expanded and updated coverage, along with new content that covers advances in the field since the previous edition published in 2009. Subject of note include updates in the fields of multidimensional and megavariate data analysis, omics data analysis, big chemical and biochemical data analysis, data fusion and sparse methods. The book follows a similar structure to the previous edition, using the same section titles to frame articles. Many chapters from the previous edition are updated, but there are also many new chapters on the latest developments. Presents integrated reviews of each chemical and biological method, examining their merits and limitations through practical examples and extensive visuals Bridges a gap in knowledge, covering developments in the field since the first edition published in 2009 Meticulously organized, with articles split into 4 sections and 12 sub-sections on key topics to allow students, researchers and professionals to find relevant information quickly and easily Written by academics and practitioners from various fields and regions to ensure that the knowledge within is easily understood and applicable to a large audience Presents integrated reviews of each chemical and biological method, examining their merits and limitations through practical examples and extensive visuals Bridges a gap in knowledge, covering developments in the field since the first edition published in 2009 Meticulously organized, with articles split into 4 sections and 12 sub-sections on key topics to allow students, researchers and professionals to find relevant information quickly and easily Written by academics and practitioners from various fields and regions to ensure that the knowledge within is easily understood and applicable to a large audience
Author: Matthias Kaeding Publisher: Springer ISBN: 365808393X Category : Mathematics Languages : en Pages : 117
Book Description
Matthias Kaeding discusses Bayesian methods for analyzing discrete and continuous failure times where the effect of time and/or covariates is modeled via P-splines and additional basic function expansions, allowing the replacement of linear effects by more general functions. The MCMC methodology for these models is presented in a unified framework and applied on data sets. Among others, existing algorithms for the grouped Cox and the piecewise exponential model under interval censoring are combined with a data augmentation step for the applications. The author shows that the resulting Gibbs sampler works well for the grouped Cox and is merely adequate for the piecewise exponential model.
Author: STANFORD UNIV CA DEPT OF STATISTICS.
Author: STANFORD UNIV CA DEPT OF STATISTICS.
Author: Genshiro Kitagawa
Author: David Brillinger
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Author: 
Author: Helcio R.B. Orlande
Author: 
Author: 
Author: Steven Brown
Author: Matthias Kaeding