Download or read book Bayesian Wavelet Shrinkage in Transformation Based Linear Models written by Shubhankar Ray and published by . This book was released on 2002 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Contributions to Bayesian Wavelet Shrinkage written by Norbert Remenyi and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis provides contributions to research in Bayesian modeling and shrinkage in the wavelet domain. Wavelets are a powerful tool to describe phenomena rapidly changing in time, and wavelet-based modeling has become a standard technique in many areas of statistics, and more broadly, in sciences and engineering. Bayesian modeling and estimation in the wavelet domain have found useful applications in nonparametric regression, image denoising, and many other areas. In this thesis, we build on the existing : techniques and propose new methods for applications in nonparametric regression, image denoising, and partially linear models. The thesis consists of an overview chapter and four main topics. In Chapter 1, we provide an overview of recent developments and the current status of Bayesian wavelet shrinkage research. The chapter contains an extensive literature review consisting of almost 100 references. The main focus of the overview chapter is on nonparametric regression, where the observations come from an unknown function contaminated with Gaussian noise. We present many methods which employ model-based and adaptive shrinkage of the wavelet coefficients through Bayes rules. These includes new developments such as dependence models, complex wavelets, and Markov chain Monte Carlo (MCMC) strategies. Some applications of Bayesian wavelet shrinkage, such as curve classification, are discussed. In Chapter 2, we propose the Gibbs Sampling Wavelet Smoother (GSWS), an adaptive wavelet denoising methodology. We use the traditional mixture prior on the wavelet coefficients, but also formulate a fully Bayesian hierarchical model in the wavelet domain accounting for the uncertainty of the prior parameters by placing hyperpriors on them. Since a closed-form solution to the Bayes estimator does not exist, the procedure is computational, in which the posterior mean is computed via MCMC simulations. We show how to efficiently develop a Gibbs sampling algorithm for the proposed model. The developed procedure is fully Bayesian, is adaptive to the underlying signal, and provides good denoising performance compared to state-of-the-art methods. Application of the method is illustrated on a real data set arising from the analysis of metabolic pathways, where an iterative shrinkage procedure is developed to preserve the mass balance of the metabolites in the system. We also show how the methodology can be extended to complex wavelet bases. In Chapter 3, we propose a wavelet-based denoising methodology based on a Bayesian hierarchical model using a double Weibull prior. The interesting feature is that in contrast to the mixture priors traditionally used by some state-of-the-art methods, the wavelet coefficients are modeled by a single density. Two estimators are developed, one based on the posterior mean and the other based on the larger posterior mode; and we show how to calculate these estimators efficiently. The methodology provides good denoising performance, comparable even to state-of-the-art methods that use a mixture prior and an empirical Bayes setting of hyperparameters; this is demonstrated by simulations on standard test functions. An application to a real-word data set is also considered. In Chapter 4, we propose a wavelet shrinkage method based on a neighborhood of wavelet coefficients, which includes two neighboring coefficients and a parental coefficient. The methodology is called Lambda-neighborhood wavelet : shrinkage, motivated by the shape of the considered neighborhood. We propose a Bayesian hierarchical model using a contaminated exponential prior on the total mean energy in the Lambda-neighborhood. The hyperparameters in the model are estimated by the empirical Bayes method, and the posterior mean, median, and Bayes factor are obtained and used in the estimation of the total mean energy. Shrinkage of the neighboring coefficients is based on the ratio of the estimated and observed energy. The proposed methodology is comparable and often superior to several established wavelet denoising methods that utilize neighboring information, which is demonstrated by extensive simulations. An application to a real-world data set from inductance plethysmography is considered, and an extension to image denoising is discussed. In Chapter 5, we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for nonparametric components with various degrees of smoothness. A hierarchical Bayes model is formulated on the parameters of this representation, where the estimation and variable selection is performed by a Gibbs sampling procedure. For both the parametric and nonparametric part of the model we are using point-mass-at-zero contamination priors with a double exponential spread distribution. In this sense we extend the model of Chapter 2 to partially linear models. Only a few papers in the area of partially linear wavelet models exist, and we show that the proposed methodology is often superior to the existing methods with respect to the task of estimating model parameters. Moreover, the method is able to perform Bayesian variable selection by a stochastic search for the parametric part of the model.

Download or read book Bayesian Inference in Wavelet Based Models written by Peter Müller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an overview of Bayesian methods for inference in the wavelet domain. The papers in this volume are divided into six parts: The first two papers introduce basic concepts. Chapters in Part II explore different approaches to prior modeling, using independent priors. Papers in the Part III discuss decision theoretic aspects of such prior models. In Part IV, some aspects of prior modeling using priors that account for dependence are explored. Part V considers the use of 2-dimensional wavelet decomposition in spatial modeling. Chapters in Part VI discuss the use of empirical Bayes estimation in wavelet based models. Part VII concludes the volume with a discussion of case studies using wavelet based Bayesian approaches. The cooperation of all contributors in the timely preparation of their manuscripts is greatly recognized. We decided early on that it was impor tant to referee and critically evaluate the papers which were submitted for inclusion in this volume. For this substantial task, we relied on the service of numerous referees to whom we are most indebted. We are also grateful to John Kimmel and the Springer-Verlag referees for considering our proposal in a very timely manner. Our special thanks go to our spouses, Gautami and Draga, for their support.

Download or read book Statistical Modeling by Wavelets written by Brani Vidakovic and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, step-by-step introduction to wavelets in statistics. What are wavelets? What makes them increasingly indispensable in statistical nonparametrics? Why are they suitable for "time-scale" applications? How are they used to solve such problems as denoising, regression, or density estimation? Where can one find up-to-date information on these newly "discovered" mathematical objects? These are some of the questions Brani Vidakovic answers in Statistical Modeling by Wavelets. Providing a much-needed introduction to the latest tools afforded statisticians by wavelet theory, Vidakovic compiles, organizes, and explains in depth research data previously available only in disparate journal articles. He carefully balances both statistical and mathematical techniques, supplementing the material with a wealth of examples, more than 100 illustrations, and extensive references-with data sets and S-Plus wavelet overviews made available for downloading over the Internet. Both introductory and data-oriented modeling topics are featured, including: * Continuous and discrete wavelet transformations. * Statistical optimality properties of wavelet shrinkage. * Theoretical aspects of wavelet density estimation. * Bayesian modeling in the wavelet domain. * Properties of wavelet-based random functions and densities. * Several novel and important wavelet applications in statistics. * Wavelet methods in time series. Accessible to anyone with a background in advanced calculus and algebra, Statistical Modeling by Wavelets promises to become the standard reference for statisticians and engineers seeking a comprehensive introduction to an emerging field.

Download or read book Practical Nonparametric and Semiparametric Bayesian Statistics written by Dipak D. Dey and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compilation of original articles by Bayesian experts, this volume presents perspectives on recent developments on nonparametric and semiparametric methods in Bayesian statistics. The articles discuss how to conceptualize and develop Bayesian models using rich classes of nonparametric and semiparametric methods, how to use modern computational tools to summarize inferences, and how to apply these methodologies through the analysis of case studies.

Download or read book Bayesian Shrinkage in Linear Models with an Application to Genetic Networks written by Dler Khidhr and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Wavelet Analysis and Active Media Technology in 3 Volumes written by Jian Ping Li and published by World Scientific Publishing Company Incorporated. This book was released on 2005 with total page 1668 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelet analysis and its applications have been one of the fastest growing research areas in the past several years. Wavelet theory has been employed in numerous fields and applications, such as signal and image processing, communication systems, biomedical imaging, radar, air acoustics, and many other areas. Active media technology is concerned with the development of autonomous computational or physical entities capable of perceiving, reasoning, adapting, learning, cooperating, and delegating in a dynamic environment.This book captures the essence of the current state of the art in wavelet analysis and active media technology. It includes nine invited papers by distinguished researchers: P Zhang, T D Bui and C Y Suen from Concordia University, Canada; N A Strelkov and V L Dol'nikov from Yaroslavl State University, Russia; Chin-Chen Chang and Ching-Yun Chang from Taiwan; S S Pandey from R D University, India; and I L Bloshanskii from Moscow State Regional University, Russia.The proceedings have been selected for coverage in:

Download or read book Emerging Technologies in Intelligent Applications for Image and Video Processing written by Santhi, V. and published by IGI Global. This book was released on 2016-01-07 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Image and Video Processing is an active area of research due to its potential applications for solving real-world problems. Integrating computational intelligence to analyze and interpret information from image and video technologies is an essential step to processing and applying multimedia data. Emerging Technologies in Intelligent Applications for Image and Video Processing presents the most current research relating to multimedia technologies including video and image restoration and enhancement as well as algorithms used for image and video compression, indexing and retrieval processes, and security concerns. Featuring insight from researchers from around the world, this publication is designed for use by engineers, IT specialists, researchers, and graduate level students.

Download or read book Brain Imaging Methods Editor s Pick 2021 written by Vince D. Calhoun and published by Frontiers Media SA. This book was released on 2021-07-01 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advances in Neural Networks ISNN 2004 written by Fuliang Yin and published by Springer. This book was released on 2011-04-07 with total page 1054 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the International Symposium on Neural N- works (ISNN 2004) held in Dalian, Liaoning, China duringAugust 19–21, 2004. ISNN 2004 received over 800 submissions from authors in ?ve continents (Asia, Europe, North America, South America, and Oceania), and 23 countries and regions (mainland China, Hong Kong, Taiwan, South Korea, Japan, Singapore, India, Iran, Israel, Turkey, Hungary, Poland, Germany, France, Belgium, Spain, UK, USA, Canada, Mexico, - nezuela, Chile, andAustralia). Based on reviews, the Program Committee selected 329 high-quality papers for presentation at ISNN 2004 and publication in the proceedings. The papers are organized into many topical sections under 11 major categories (theo- tical analysis; learning and optimization; support vector machines; blind source sepa- tion,independentcomponentanalysis,andprincipalcomponentanalysis;clusteringand classi?cation; robotics and control; telecommunications; signal, image and time series processing; detection, diagnostics, and computer security; biomedical applications; and other applications) covering the whole spectrum of the recent neural network research and development. In addition to the numerous contributed papers, ?ve distinguished scholars were invited to give plenary speeches at ISNN 2004. ISNN 2004 was an inaugural event. It brought together a few hundred researchers, educators,scientists,andpractitionerstothebeautifulcoastalcityDalianinnortheastern China. It provided an international forum for the participants to present new results, to discuss the state of the art, and to exchange information on emerging areas and future trends of neural network research. It also created a nice opportunity for the participants to meet colleagues and make friends who share similar research interests.

Download or read book Master s Theses Directories written by and published by . This book was released on 2002 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Education, arts and social sciences, natural and technical sciences in the United States and Canada".

Download or read book Bayesian Wavelet and Fourier Transform Kernel Regression and Classification in RKHS written by Xueying Zhang and published by . This book was released on 2021 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kernel methods are often used for nonlinear regression and classification in machine learning because they are computationally cheap and accurate. Fourier basis and wavelet basis are the bases that can efficiently approximate the kernel functions. In previous research, Bayesian approximate kernel regression with Fourier transform has been proposed. With the proposed method, we use the analytic properties of the reproducing kernel Hilbert space (RKHS) to define a linear vector space that captures nonlinear structures. We map the data into a low-dimensional randomized feature space using Fourier transform and convert kernel function into operations of a linear machine. A Bayesian approximate kernel regression model is then formulated with the application of a generalized kernel model and the Bayesian method. We replace Fourier transform with wavelet transform in randomized feature space to approximate kernel functions. We formulate a new Bayesian approximate kernel model with wavelet transform and use the Gibbs sampler to compute the parameters of the model. We then make a comparison between the performance of Fourier based and wavelet-based Bayesian approximate kernels solving both regression and classification problems.

Download or read book Multiscale Signal Analysis and Modeling written by Xiaoping Shen and published by Springer Science & Business Media. This book was released on 2012-09-18 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiscale Signal Analysis and Modeling presents recent advances in multiscale analysis and modeling using wavelets and other systems. This book also presents applications in digital signal processing using sampling theory and techniques from various function spaces, filter design, feature extraction and classification, signal and image representation/transmission, coding, nonparametric statistical signal processing, and statistical learning theory.

Download or read book Bayesian Methods for Nonlinear Classification and Regression written by David G. T. Denison and published by John Wiley & Sons. This book was released on 2002-05-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A Shrinkage average Method for Fitting High Dimensional Linear Models written by Jingyi Liu and published by . This book was released on 2008 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advances in Adaptive and Deep Bayesian State space Models written by Haoxuan Wu and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work explores modeling and forecasting of time series data using a Bayesian state-space approach. Three sections are included, each describing a methodology based on Bayesian state-space framework for dealing with different challenges. The first methodology adds shrinkage and threshold estimation into a dynamic linear model to identify changepoints. The second methodology focuses on decoupling of shrinkage and modeling to provide posterior summaries. The third methodology incorporates a recurrent neural network with a state-space framework to produce robust and accurate forecasting of large datasets. While these methodologies are broadly applicable, an unifying theme is the usage of global-local shrinkage priors. In Chapter 2, we introduce global-local shrinkage priors into a Bayesian dynamic linear model to adaptively estimate both changepoints and local outliers in a novel model we call Adaptive Bayesian Changepoints with Outliers (ABCO). We utilize a state-space approach to identify a dynamic signal in the presence of outliers and measurement error with stochastic volatility. This setup provides a flexible framework to detect unspecified changepoints in complex series, such as those with large interruptions in local trends, with robustness to outliers and heteroskedastic noise. In Chapter 3, we introduce a new approach for decoupling trends (drift) and changepoints (shifts) in time series. Our locally adaptive model-based approach for robustly decoupling combines Bayesian trend filtering and machine learning based regularization. The proposed decoupling approach incorporates the strengths of both methods, i.e. the flexibility of Bayesian DLMs with the hard thresholding property of penalized likelihood estimators, to provide changepoint analysis in complex, modern settings. The proposed framework is outlier robust and can identify a variety of changes, including in mean and slope. In Chapter 4, we introduce a new version of deep state-space models (DSSMs) that combines a recurrent neural network with a state-space framework to forecast time series data. The model estimates the observed series as functions of latent variables that evolve non-linearly through time. Our paper focus on producing interpretable latent parameters with two key modifications. First, we simplify the predictive decoder by restricting the response variables to be a linear transformation of the latent variables plus some noise. Second, we utilize shrinkage priors on the latent variables to reduce redundancy and improve robustness. These changes make the latent variables much easier to understand and allow us to interpret the resulting latent variables as random effects in a linear mixed model.

Download or read book Multi Chaos Fractal and Multi Fractional Artificial Intelligence of Different Complex Systems written by Yeliz Karaca and published by Academic Press. This book was released on 2022-06-22 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies as well as applications including theoretical aspects of complexity. Foregrounding Multi-chaos, Fractal and Multi-fractional in the era of Artificial Intelligence (AI), the edited book deals with multi- chaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications, artificial intelligence, mathematics-informed and data driven processes aside from the means of modelling, and simulations for the solution of multifaceted problems characterized by nonlinearity, non-regularity and self-similarity, frequently encountered in different complex systems. The fundamental interacting components underlying complexity, complexity thinking, processes and theory along with computational processes and technologies, with machine learning as the core component of AI demonstrate the enabling of complex data to augment some critical human skills. Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the overarching aim is to empower out-of-the-box thinking through multifarious methods, directed towards paradoxical situations, uncertain processes, chaotic, transient and nonlinear dynamics of complex systems. Constructs and presents a multifarious approach for critical decision-making processes embodying paradoxes and uncertainty. Includes a combination of theory and applications with regard to multi-chaos, fractal and multi-fractional as well as AI of different complex systems and many-body systems. Provides readers with a bridge between application of advanced computational mathematical methods and AI based on comprehensive analyses and broad theories.