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Author: Ji Yeon Yang Publisher: ISBN: Category : Languages : en Pages : 44
Book Description
There has been continuing interest in Bayesian regressions without imposing any parametric assumption on the error distribution, but the asymptotic efficiency of such procedures has not been fully understood yet. In this article, we consider semiparametric Bayesian nonlinear regression models. We do not impose a parametric form for the likelihood function; rather, we treat the true density function of error terms as an infinite dimensional nuisance parameter and estimate it nonparametrically. Thereafter, we conduct conventional parametric Bayesian inference using MCMC methods. We derive the asymptotic properties of the resulting estimator and identify conditions of adaptive estimation, under which our two-step Bayes estimator enjoys the same asymptotic normality as if we knew the true density. We compare accuracy and coverage of the adaptive Bayesian estimator with the maximum likelihood estimator in empirical studies on simulated and real data. In particular, we observe that the Bayesian inference may be superior in numerical stability for small sample sizes.
Author: Ji Yeon Yang Publisher: ISBN: Category : Languages : en Pages : 44
Book Description
There has been continuing interest in Bayesian regressions without imposing any parametric assumption on the error distribution, but the asymptotic efficiency of such procedures has not been fully understood yet. In this article, we consider semiparametric Bayesian nonlinear regression models. We do not impose a parametric form for the likelihood function; rather, we treat the true density function of error terms as an infinite dimensional nuisance parameter and estimate it nonparametrically. Thereafter, we conduct conventional parametric Bayesian inference using MCMC methods. We derive the asymptotic properties of the resulting estimator and identify conditions of adaptive estimation, under which our two-step Bayes estimator enjoys the same asymptotic normality as if we knew the true density. We compare accuracy and coverage of the adaptive Bayesian estimator with the maximum likelihood estimator in empirical studies on simulated and real data. In particular, we observe that the Bayesian inference may be superior in numerical stability for small sample sizes.
Author: David G. T. Denison Publisher: John Wiley & Sons ISBN: 9780471490364 Category : Mathematics Languages : en Pages : 302
Book Description
Bei der Regressionsanalyse von Datenmaterial erhält man leider selten lineare oder andere einfache Zusammenhänge (parametrische Modelle). Dieses Buch hilft Ihnen, auch komplexere, nichtparametrische Modelle zu verstehen und zu beherrschen. Stärken und Schwächen jedes einzelnen Modells werden durch die Anwendung auf Standarddatensätze demonstriert. Verbreitete nichtparametrische Modelle werden mit Hilfe von Bayes-Verfahren in einen kohärenten wahrscheinlichkeitstheoretischen Zusammenhang gebracht.
Author: Broemeling Publisher: Routledge ISBN: 1351464477 Category : Mathematics Languages : en Pages : 480
Book Description
With Bayesian statistics rapidly becoming accepted as a way to solve applied statisticalproblems, the need for a comprehensive, up-to-date source on the latest advances in thisfield has arisen.Presenting the basic theory of a large variety of linear models from a Bayesian viewpoint,Bayesian Analysis of Linear Models fills this need. Plus, this definitive volume containssomething traditional-a review of Bayesian techniques and methods of estimation, hypothesis,testing, and forecasting as applied to the standard populations ... somethinginnovative-a new approach to mixed models and models not generally studied by statisticianssuch as linear dynamic systems and changing parameter models ... and somethingpractical-clear graphs, eary-to-understand examples, end-of-chapter problems, numerousreferences, and a distribution appendix.Comprehensible, unique, and in-depth, Bayesian Analysis of Linear Models is the definitivemonograph for statisticians, econometricians, and engineers. In addition, this text isideal for students in graduate-level courses such as linear models, econometrics, andBayesian inference.
Author: Nikolay Nikolaev Publisher: Springer Science & Business Media ISBN: 0387312404 Category : Computers Languages : en Pages : 329
Book Description
This book delivers theoretical and practical knowledge for developing algorithms that infer linear and non-linear multivariate models, providing a methodology for inductive learning of polynomial neural network models (PNN) from data. The text emphasizes an organized model identification process by which to discover models that generalize and predict well. The book further facilitates the discovery of polynomial models for time-series prediction.
Author: Xiaofeng Wang Publisher: CRC Press ISBN: 1351165755 Category : Mathematics Languages : en Pages : 312
Book Description
INLA stands for Integrated Nested Laplace Approximations, which is a new method for fitting a broad class of Bayesian regression models. No samples of the posterior marginal distributions need to be drawn using INLA, so it is a computationally convenient alternative to Markov chain Monte Carlo (MCMC), the standard tool for Bayesian inference. Bayesian Regression Modeling with INLA covers a wide range of modern regression models and focuses on the INLA technique for building Bayesian models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to demonstrate the interplay of theory and practice with reproducible studies. Complete R commands are provided for each example, and a supporting website holds all of the data described in the book. An R package including the data and additional functions in the book is available to download. The book is aimed at readers who have a basic knowledge of statistical theory and Bayesian methodology. It gets readers up to date on the latest in Bayesian inference using INLA and prepares them for sophisticated, real-world work. Xiaofeng Wang is Professor of Medicine and Biostatistics at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and a Full Staff in the Department of Quantitative Health Sciences at Cleveland Clinic. Yu Ryan Yue is Associate Professor of Statistics in the Paul H. Chook Department of Information Systems and Statistics at Baruch College, The City University of New York. Julian J. Faraway is Professor of Statistics in the Department of Mathematical Sciences at the University of Bath.
Author: Peter Guang Yi Lu Publisher: ISBN: Category : Languages : en Pages : 175
Book Description
A new methodology for Bayesian inference of stochastic dynamical models is developed. The methodology leverages the dynamically orthogonal (DO) evolution equations for reduced-dimension uncertainty evolution and the Gaussian mixture model DO filtering algorithm for nonlinear reduced-dimension state variable inference to perform parallelized computation of marginal likelihoods for multiple candidate models, enabling efficient Bayesian update of model distributions. The methodology also employs reduced-dimension state augmentation to accommodate models featuring uncertain parameters. The methodology is applied successfully to two high-dimensional, nonlinear simulated fluid and ocean systems. Successful joint inference of an uncertain spatial geometry, one uncertain model parameter, and [Omicron](105) uncertain state variables is achieved for the first. Successful joint inference of an uncertain stochastic dynamical equation and [Omicron](105) uncertain state variables is achieved for the second. Extensions to adaptive modeling and adaptive sampling are discussed.
Author: David D. Denison Publisher: Springer Science & Business Media ISBN: 0387215794 Category : Mathematics Languages : en Pages : 465
Book Description
Researchers in many disciplines face the formidable task of analyzing massive amounts of high-dimensional and highly-structured data. This is due in part to recent advances in data collection and computing technologies. As a result, fundamental statistical research is being undertaken in a variety of different fields. Driven by the complexity of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern "data analysis," a term that we liberally interpret to include speech and pattern recognition, classification, data compression and signal processing. The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics. The proposed workshop intends to bring together eminent experts from these fields in order to exchange ideas and forge directions for the future.
Author: Yanan Fan Publisher: Academic Press ISBN: 0128158638 Category : Business & Economics Languages : en Pages : 302
Book Description
Flexible Bayesian Regression Modeling is a step-by-step guide to the Bayesian revolution in regression modeling, for use in advanced econometric and statistical analysis where datasets are characterized by complexity, multiplicity, and large sample sizes, necessitating the need for considerable flexibility in modeling techniques. It reviews three forms of flexibility: methods which provide flexibility in their error distribution; methods which model non-central parts of the distribution (such as quantile regression); and finally models that allow the mean function to be flexible (such as spline models). Each chapter discusses the key aspects of fitting a regression model. R programs accompany the methods. This book is particularly relevant to non-specialist practitioners with intermediate mathematical training seeking to apply Bayesian approaches in economics, biology, finance, engineering and medicine. Introduces powerful new nonparametric Bayesian regression techniques to classically trained practitioners Focuses on approaches offering both superior power and methodological flexibility Supplemented with instructive and relevant R programs within the text Covers linear regression, nonlinear regression and quantile regression techniques Provides diverse disciplinary case studies for correlation and optimization problems drawn from Bayesian analysis ‘in the wild’
Author: Ji Yeon Yang
Author: Ji Yeon Yang
Author: David G. T. Denison
Author: Broemeling
Author: Nikolay Nikolaev
Author: Xiaofeng Wang
Author: Yaqi Yang
Author: Peter Guang Yi Lu
Author: David D. Denison
Author: Yanan Fan
Author: Clemens Biller