Download or read book Nonparametric Bayesian Methods for Evaluating Fit in Hierarchical Models written by Kert Viele and published by . This book was released on 1996 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Nonparametrics written by J.K. Ghosh and published by Springer Science & Business Media. This book was released on 2006-05-11 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. It will also appeal to statisticians in general. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian non-parametrics.
Download or read book Bayesian Nonparametric Data Analysis written by Peter Müller and published by Springer. This book was released on 2015-06-17 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in online software pages.
Download or read book Bayesian Nonparametrics via Neural Networks written by Herbert K. H. Lee and published by SIAM. This book was released on 2004-01-01 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Nonparametrics via Neural Networks is the first book to focus on neural networks in the context of nonparametric regression and classification, working within the Bayesian paradigm. Its goal is to demystify neural networks, putting them firmly in a statistical context rather than treating them as a black box. This approach is in contrast to existing books, which tend to treat neural networks as a machine learning algorithm instead of a statistical model. Once this underlying statistical model is recognized, other standard statistical techniques can be applied to improve the model. The Bayesian approach allows better accounting for uncertainty. This book covers uncertainty in model choice and methods to deal with this issue, exploring a number of ideas from statistics and machine learning. A detailed discussion on the choice of prior and new noninformative priors is included, along with a substantial literature review. Written for statisticians using statistical terminology, Bayesian Nonparametrics via Neural Networks will lead statisticians to an increased understanding of the neural network model and its applicability to real-world problems.
Download or read book On Nonparametric Bayesian Hierarchical Modelling written by Liping Liu and published by . This book was released on 1996 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Nonparametrics written by Nils Lid Hjort and published by Cambridge University Press. This book was released on 2010-04-12 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian nonparametrics works - theoretically, computationally. The theory provides highly flexible models whose complexity grows appropriately with the amount of data. Computational issues, though challenging, are no longer intractable. All that is needed is an entry point: this intelligent book is the perfect guide to what can seem a forbidding landscape. Tutorial chapters by Ghosal, Lijoi and Prünster, Teh and Jordan, and Dunson advance from theory, to basic models and hierarchical modeling, to applications and implementation, particularly in computer science and biostatistics. These are complemented by companion chapters by the editors and Griffin and Quintana, providing additional models, examining computational issues, identifying future growth areas, and giving links to related topics. This coherent text gives ready access both to underlying principles and to state-of-the-art practice. Specific examples are drawn from information retrieval, NLP, machine vision, computational biology, biostatistics, and bioinformatics.
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 Bayesian Data Analysis Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
Download or read book Encyclopedia of Statistical Sciences Volume 15 written by and published by John Wiley & Sons. This book was released on 2005-12-16 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: ENCYCLOPEDIA OF STATISTICAL SCIENCES
Download or read book Nonlinear Mixture Models A Bayesian Approach written by Tatiana V Tatarinova and published by World Scientific. This book was released on 2014-12-30 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by two mathematicians from the University of Southern California, provides a broad introduction to the important subject of nonlinear mixture models from a Bayesian perspective. It contains background material, a brief description of Markov chain theory, as well as novel algorithms and their applications. It is self-contained and unified in presentation, which makes it ideal for use as an advanced textbook by graduate students and as a reference for independent researchers. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.In this book the authors present Bayesian methods of analysis for nonlinear, hierarchical mixture models, with a finite, but possibly unknown, number of components. These methods are then applied to various problems including population pharmacokinetics and gene expression analysis. In population pharmacokinetics, the nonlinear mixture model, based on previous clinical data, becomes the prior distribution for individual therapy. For gene expression data, one application included in the book is to determine which genes should be associated with the same component of the mixture (also known as a clustering problem). The book also contains examples of computer programs written in BUGS. This is the first book of its kind to cover many of the topics in this field.
Download or read book Bayesian Nonparametric Models for Name Disambiguation and Supervised Learning written by Andrew Mingbo Dai and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents new Bayesian nonparametric models and approaches for their development, for the problems of name disambiguation and supervised learning. Bayesian nonparametric methods form an increasingly popular approach for solving problems that demand a high amount of model flexibility. However, this field is relatively new, and there are many areas that need further investigation. Previous work on Bayesian nonparametrics has neither fully explored the problems of entity disambiguation and supervised learning nor the advantages of nested hierarchical models. Entity disambiguation is a widely encountered problem where different references need to be linked to a real underlying entity. This problem is often unsupervised as there is no previously known information about the entities. Further to this, effective use of Bayesian nonparametrics offer a new approach to tackling supervised problems, which are frequently encountered. The main original contribution of this thesis is a set of new structured Dirichlet process mixture models for name disambiguation and supervised learning that can also have a wide range of applications. These models use techniques from Bayesian statistics, including hierarchical and nested Dirichlet processes, generalised linear models, Markov chain Monte Carlo methods and optimisation techniques such as BFGS. The new models have tangible advantages over existing methods in the field as shown with experiments on real-world datasets including citation databases and classification and regression datasets. I develop the unsupervised author-topic space model for author disambiguation that uses free-text to perform disambiguation unlike traditional author disambiguation approaches. The model incorporates a name variant model that is based on a nonparametric Dirichlet language model. The model handles both novel unseen name variants and can model the unknown authors of the text of the documents. Through this, the model can disambiguate authors with no prior knowledge of the number of true authors in the dataset. In addition, it can do this when the authors have identical names. I use a model for nesting Dirichlet processes named the hybrid NDP-HDP. This model allows Dirichlet processes to be clustered together and adds an additional level of structure to the hierarchical Dirichlet process. I also develop a new hierarchical extension to the hybrid NDP-HDP. I develop this model into the grouped author-topic model for the entity disambiguation task. The grouped author-topic model uses clusters to model the co-occurrence of entities in documents, which can be interpreted as research groups. Since this model does not require entities to be linked to specific words in a document, it overcomes the problems of some existing author-topic models. The model incorporates a new method for modelling name variants, so that domain-specific name variant models can be used. Lastly, I develop extensions to supervised latent Dirichlet allocation, a type of supervised topic model. The keyword-supervised LDA model predicts document responses more accurately by modelling the effect of individual words and their contexts directly. The supervised HDP model has more model flexibility by using Bayesian nonparametrics for supervised learning. These models are evaluated on a number of classification and regression problems, and the results show that they outperform existing supervised topic modelling approaches. The models can also be extended to use similar information to the previous models, incorporating additional information such as entities and document titles to improve prediction.
Download or read book Bayesian Methods written by Jeff Gill and published by CRC Press. This book was released on 2007-11-26 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of Bayesian Methods: A Social and Behavioral Sciences Approach helped pave the way for Bayesian approaches to become more prominent in social science methodology. While the focus remains on practical modeling and basic theory as well as on intuitive explanations and derivations without skipping steps, this second edition incorpora
Download or read book Nonparametric Bayesian Models for Unsupervised Learning written by Pu Wang and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unsupervised learning is an important topic in machine learning. In particular, clustering is an unsupervised learning problem that arises in a variety of applications for data analysis and mining. Unfortunately, clustering is an ill-posed problem and, as such, a challenging one: no ground-truth that can be used to validate clustering results is available. Two issues arise as a consequence. Various clustering algorithms embed their own bias resulting from different optimization criteria. As a result, each algorithm may discover different patterns in a given dataset. The second issue concerns the setting of parameters. In clustering, parameter setting controls the characterization of individual clusters, and the total number of clusters in the data. Clustering ensembles have been proposed to address the issue of different biases induced by various algorithms. Clustering ensembles combine different clustering results, and can provide solutions that are robust against spurious elements in the data. Although clustering ensembles provide a significant advance, they do not address satisfactorily the model selection and the parameter tuning problem. Bayesian approaches have been applied to clustering to address the parameter tuning and model selection issues. Bayesian methods provide a principled way to address these problems by assuming prior distributions on model parameters. Prior distributions assign low probabilities to parameter values which are unlikely. Therefore they serve as regularizers for modeling parameters, and can help avoid over-fitting. In addition, the marginal likelihood is used by Bayesian approaches as the criterion for model selection. Although Bayesian methods provide a principled way to perform parameter tuning and model selection, the key question \How many clusters?" is still open. This is a fundamental question for model selection. A special kind of Bayesian methods, nonparametric Bayesian approaches, have been proposed to address this important model selection issue. Unlike parametric Bayesian models, for which the number of parameters is finite and fixed, nonparametric Bayesian models allow the number of parameters to grow with the number of observations. After observing the data, nonparametric Bayesian models t the data with finite dimensional parameters. An additional issue with clustering is high dimensionality. High-dimensional data pose a difficult challenge to the clustering process. A common scenario with high-dimensional data is that clusters may exist in different subspaces comprised of different combinations of features (dimensions). In other words, data points in a cluster may be similar to each other along a subset of dimensions, but not in all dimensions. People have proposed subspace clustering techniques, a.k.a. co-clustering or bi-clustering, to address the dimensionality issue (here, I use the term co-clustering). Like clustering, also co-clustering suffers from the ill-posed nature and the lack of ground-truth to validate the results. Although attempts have been made in the literature to address individually the major issues related to clustering, no previous work has addressed them jointly. In my dissertation I propose a unified framework that addresses all three issues at the same time. I designed a nonparametric Bayesian clustering ensemble (NBCE) approach, which assumes that multiple observed clustering results are generated from an unknown consensus clustering. The under- lying distribution is assumed to be a mixture distribution with a nonparametric Bayesian prior, i.e., a Dirichlet Process. The number of mixture components, a.k.a. the number of consensus clusters, is learned automatically. By combining the ensemble methodology and nonparametric Bayesian modeling, NBCE addresses both the ill-posed nature and the parameter setting/model selection issues of clustering. Furthermore, NBCE outperforms individual clustering methods, since it can escape local optima by combining multiple clustering results. I also designed a nonparametric Bayesian co-clustering ensemble (NBCCE) technique. NBCCE inherits the advantages of NBCE, and in addition it is effective with high dimensional data. As such, NBCCE provides a unified framework to address all the three aforementioned issues. NBCCE assumes that multiple observed co-clustering results are generated from an unknown consensus co-clustering. The underlying distribution is assumed to be a mixture with a nonparametric Bayesian prior. I developed two models to generate co-clusters in terms of row- and column- clusters. In one case row- and column-clusters are assumed to be independent, and NBCCE assumes two independent Dirichlet Process priors on the hidden consensus co-clustering, one for rows and one for columns. The second model captures the dependence between row- and column-clusters by assuming a Mondrian Process prior on the hidden consensus co-clustering. Combined with Mondrian priors, NBCCE provides more flexibility to fit the data. I have performed extensive evaluation on relational data and protein-molecule interaction data. The empirical evaluation demonstrates the effectiveness of NBCE and NBCCE and their advantages over traditional clustering and co-clustering methods.
Download or read book Computing Bayesian Nonparametric Hierarchical Models written by Michael D. Escobar and published by . This book was released on 1992 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Hierarchical Models written by Peter D. Congdon and published by CRC Press. This book was released on 2019-09-16 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: An intermediate-level treatment of Bayesian hierarchical models and their applications, this book demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables, and in methods where parameters can be treated as random collections. Through illustrative data analysis and attention to statistical computing, this book facilitates practical implementation of Bayesian hierarchical methods. The new edition is a revision of the book Applied Bayesian Hierarchical Methods. It maintains a focus on applied modelling and data analysis, but now using entirely R-based Bayesian computing options. It has been updated with a new chapter on regression for causal effects, and one on computing options and strategies. This latter chapter is particularly important, due to recent advances in Bayesian computing and estimation, including the development of rjags and rstan. It also features updates throughout with new examples. The examples exploit and illustrate the broader advantages of the R computing environment, while allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. Features: Provides a comprehensive and accessible overview of applied Bayesian hierarchical modelling Includes many real data examples to illustrate different modelling topics R code (based on rjags, jagsUI, R2OpenBUGS, and rstan) is integrated into the book, emphasizing implementation Software options and coding principles are introduced in new chapter on computing Programs and data sets available on the book’s website
Download or read book Robust Statistical Modeling Through Nonparametric Bayesian Methods written by Ju Hee Lee and published by . This book was released on 2010 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Nonparametric Bayesian models are commonly used to obtain robust statistical inference, and the most popular nonparametric Bayesian model is, arguably, the mixture of Dirichlet processes (MDP) model. In this study, we examine the question of how to obtain more robustness than under a conventional MDP model. In answer to this question, we develop two models from a nonparametric Bayesian viewpoint, and we investigate their properties: (i) the limiting Dirichlet process (limdir) model, and (ii) the local-mass preserving mixture of Dirichlet process (LMDP) model. The limdir model addresses the question of how to perform a ``noninformative" nonparametric Bayesian analysis. Rather than being noninformative, the model requires a slight amount of input, and so provides us with a minimally informative prior distribution with which to conduct a nonparametric Bayesian analysis. The limdir prior distribution can be viewed as the limit of a sequence of mixture of Dirichlet process models. This model requires only modest input, and yet provides posterior behavior which has a number of important qualitative features, including robustness. Second, the LMDP prior distribution focuses on local mass (defined in the paper). To specify such a prior distribution, we carefully consider the behavior of parameters of interest in some small region, and we then select a prior distribution which preserves mass in the region. Local mass preservation ties the mass of the base measure to its dispersion, resulting in robust inference. These two strategies for constructing a prior distribution can be applied to any model based on the Dirichlet process. Calibration of the prior distribution is considered. We use the limdir for the compound decision problem and the one-way analysis of variance problem, and compare its performance to that of mixture of Dirichlet processes models and to parametric Bayesian models on actual data sets. We apply the LMDP model for the one-way analysis of variance problem, and compare its performance to that of a mixture of Dirichlet processes model with a conventional prior structure. In addition to developing the robust nonparametric Bayesian models, the latter part of the study describes a general form of consistency which does not necessarily rely on correct specification of the likelihood. We carefully investigate issues of consistency and inconsistency for a variety of functions of interest, such as equality of subsets of treatment means, without the assumption that the model is correct. We prove that Bayes estimators achieve (asymptotic) consistency under some suitable regularity conditions on the assumed likelihood. More importantly, we find a need to distinguish between the notions of two parameters being "equal to one another" and "close to one another", and we illustrate differences in asymptotic inference for these two statements. This distinction carries with it implications for Bayesian tests of a point null hypothesis.
Download or read book The Oxford Handbook of Applied Bayesian Analysis written by Anthony O' Hagan and published by OUP Oxford. This book was released on 2010-03-18 with total page 924 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian analysis has developed rapidly in applications in the last two decades and research in Bayesian methods remains dynamic and fast-growing. Dramatic advances in modelling concepts and computational technologies now enable routine application of Bayesian analysis using increasingly realistic stochastic models, and this drives the adoption of Bayesian approaches in many areas of science, technology, commerce, and industry. This Handbook explores contemporary Bayesian analysis across a variety of application areas. Chapters written by leading exponents of applied Bayesian analysis showcase the scientific ease and natural application of Bayesian modelling, and present solutions to real, engaging, societally important and demanding problems. The chapters are grouped into five general areas: Biomedical & Health Sciences; Industry, Economics & Finance; Environment & Ecology; Policy, Political & Social Sciences; and Natural & Engineering Sciences, and Appendix material in each touches on key concepts, models, and techniques of the chapter that are also of broader pedagogic and applied interest.
