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 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 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 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 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 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 Hierarchical Bayesian Nonparametric Models for Power law Sequences written by Jan Alexander Gasthaus 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 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 Nonparametric Bayesian Inference in Biostatistics written by Riten Mitra and published by Springer. This book was released on 2015-07-25 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: As chapters in this book demonstrate, BNP has important uses in clinical sciences and inference for issues like unknown partitions in genomics. Nonparametric Bayesian approaches (BNP) play an ever expanding role in biostatistical inference from use in proteomics to clinical trials. Many research problems involve an abundance of data and require flexible and complex probability models beyond the traditional parametric approaches. As this book's expert contributors show, BNP approaches can be the answer. Survival Analysis, in particular survival regression, has traditionally used BNP, but BNP's potential is now very broad. This applies to important tasks like arrangement of patients into clinically meaningful subpopulations and segmenting the genome into functionally distinct regions. This book is designed to both review and introduce application areas for BNP. While existing books provide theoretical foundations, this book connects theory to practice through engaging examples and research questions. Chapters cover: clinical trials, spatial inference, proteomics, genomics, clustering, survival analysis and ROC curve.

Download or read book Nonparametric Hierarchical Bayesian Models of Categorization written by Kevin Canini and published by . This book was released on 2011 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Categorization, or classification, is a fundamental problem in both cognitive psychology and machine learning. Classical psychological models of categorization fall into two main groups: prototype models and exemplar models, which are equivalent, respectively, to the statistical methods of parametric density estimation and kernel density estimation. Many categorization studies in psychology attempt to understand how people solve this problem by comparing their inferences to those of formal computational models such as prototype or exemplar models. From this perspective, different models make different predictions about the representations and mechanisms people use to make categorization judgments. Instead, one can seek to understand categorization by viewing it as a problem of statistical inference and attempting to characterize the inductive biases of human learners. These inductive biases can be directly exposed using an experimental method called iterated learning, which provides direct insight into human categorization in a way that is independent of any proposed models. I describe the results of an iterated learning study of human categorization which supports previous findings by psychologists that people's representations seem to be more flexible than would be implied by either prototype or exemplar models alone. Prototype and exemplar models both use a single, fixed level of complexity in their representations of categories, with prototype models exhibiting the simplest representations, and exemplar models using the most complex representations. Treating categorization as a type of statistical inference, I describe a family of nonparametric Bayesian models of categorization based on the Dirichlet process mixture model (DPMM). These models represent categories as combinations of clusters of objects and, together, produce a continuum of representational complexities where prototype and exemplar models are special cases, occupying opposite ends of the spectrum. DPMM models allow the level of complexity of category representations to be chosen to suit the task at hand or to change over time; this flexibility can explain psychological results demonstrating that people's inferences are more congruent with prototype models at some times and exemplar models at other times. The DPMM can be generalized into a larger framework of models based on the hierarchical Dirichlet process (HDP). The HDP subsumes the DPMM and multiple previous psychological models, including prototypes, exemplars, and the Rational Model of Categorization. In addition, the HDP contains a family of previously unexplored models which make interesting predictions about how information can be shared between multiple categories. While most other categorization models learn each individual category in isolation and independently of the others, these HDP models share information between categories. This sharing of information can improve the speed and accuracy of learning and explained certain transfer learning effects that were observed in people's judgments. I introduce an extension of the HDP, called the tree-HDP, which is designed to infer systems of hierarchically related categories. The tree-HDP is able to simultaneously learn categories at multiple levels of generality and infer the taxonomic relationships between them. The original scientific contributions of this dissertation are a detailed characterization of the inductive biases of human categorization via iterated learning, a unification of previous psychological models of categorization into a common Bayesian statistical framework (the HDP), a demonstration that this framework contains interesting and previously unexplored models that predict and explain the integration of information from multiple categories, and a proposal and exploration of a new statistical model, the tree-HDP, which can simultaneously learn categories at multiple hierarchical levels and infer taxonomic relationships between those categories.

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 580 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 Applied Bayesian Hierarchical Methods written by Peter D. Congdon and published by CRC Press. This book was released on 2010-05-19 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of Markov chain Monte Carlo (MCMC) methods for estimating hierarchical models involves complex data structures and is often described as a revolutionary development. An intermediate-level treatment of Bayesian hierarchical models and their applications, Applied Bayesian Hierarchical Methods demonstrates the advantages of a Bayesian approach

Download or read book Bayesian Hierarchical Semiparametric and Nonparametric Methods for International New Product Diffusion written by Brian Matthew Hartman and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Global marketing managers are keenly interested in being able to predict the sales of their new products. Understanding how a product is adopted over time allows the managers to optimally allocate their resources. With the world becoming ever more global, there are strong and complex interactions between the countries in the world. My work explores how to describe the relationship between those countries and determines the best way to leverage that information to improve the sales predictions. In Chapter II, I describe how diffusion speed has changed over time. The most recent major study on this topic, by Christophe Van den Bulte, investigated new product di ffusions in the United States. Van den Bulte notes that a similar study is needed in the international context, especially in developing countries. Additionally, his model contains the implicit assumption that the diffusion speed parameter is constant throughout the life of a product. I model the time component as a nonparametric function, allowing the speed parameter the flexibility to change over time. I find that early in the product's life, the speed parameter is higher than expected. Additionally, as the Internet has grown in popularity, the speed parameter has increased. In Chapter III, I examine whether the interactions can be described through a reference hierarchy in addition to the cross-country word-of-mouth eff ects already in the literature. I also expand the word-of-mouth e ffect by relating the magnitude of the e ffect to the distance between the two countries. The current literature only applies that e ffect equally to the n closest countries (forming a neighbor set). This also leads to an analysis of how to best measure the distance between two countries. I compare four possible distance measures: distance between the population centroids, trade ow, tourism ow, and cultural similarity. Including the reference hierarchy improves the predictions by 30 percent over the current best model. Finally, in Chapter IV, I look more closely at the Bass Diffusion Model. It is prominently used in the marketing literature and is the base of my analysis in Chapter III. All of the current formulations include the implicit assumption that all the regression parameters are equal for each country. One dollar increase in GDP should have more of an eff ect in a poor country than in a rich country. A Dirichlet process prior enables me to cluster the countries by their regression coefficients. Incorporating the distance measures can improve the predictions by 35 percent in some cases.

Download or read book Aspects of Uncertainty written by Adrian F. M. Smith and published by . This book was released on 1994-09-13 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Throughout his career Dennis Lindley has insisted on thinking things through from first principles and on basing developments on firm, logical foundations. Although his fundamental contributions to Bayesian statistics and decision theory are universally recognised, it is less well known that he arrived at the Bayesian position as a result of seeking to establish a rigorous axiomatic justification for classical statistical procedures.

Download or read book Bayesian Theory and Applications written by Paul Damien and published by Oxford University Press. This book was released on 2013-01-24 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances 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.