Download or read book Bayesian Variable Selection and Hypothesis Testing written by Su Chen (Ph. D.) and published by . This book was released on 2020 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: In modern statistical and machine learning applications, there is an increasing need for developing methodologies and algorithms to analyze massive data sets. Coupled with the growing popularity of Bayesian methods in statistical analysis, range of new techniques have evolved that allow innovative model-building and inference. In this dissertation, we develop Bayesian methods for variable selection and hypothesis testing. One important theme of this work is to develop computationally efficient algorithms that also enjoy strong probabilistic guarantees of convergence in a frequentist sense. Another equally important theme is to bridge the gap of classical statistical inference and Bayesian inference, in particular, through a new approach of hypothesis testing which can justify the Bayesian interpretation of classical testing framework. These methods are validated and demonstrated through simulated examples and real data applications
Download or read book Bayesian Hypothesis Testing and Variable Selection in High Dimensional Regression written by Min Wang and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: This dissertation consists of three distinct but related research projects. First of all, we study the Bayesian approach to model selection in the class of normal regression models. We propose an explicit closed-form expression of the Bayes factor with the use of Zellner's g-prior and the beta-prime prior for g. Noting that linear models with a growing number of unknown parameters have recently gained increasing popularity in practice, such as the spline problem, we shall thus be particularly interested in studying the model selection consistency of the Bayes factor under the scenario in which the dimension of the parameter space increases with the sample size. Our results show that the proposed Bayes factor is always consistent under the null model and is consistent under the alternative model except for a small set of alternative models which can be characterized. It is noteworthy that the results mentioned above can be applied to the analysis of variance (ANOVA) model, which has been widely used in many areas of science, such as ecology, psychology, and behavioral research. For the one-way unbalanced ANOVA model, we propose an explicit closed-form expression of the Bayes factor which is thus easy to compute. In addition, its corresponding model selection consistency has been investigated under different asymptotic situations. For the one-way random effects models, we also propose a closed-form Bayes factor without integral representation which has reasonable model selection consistency under different asymptotic scenarios. Moreover, the performance of the proposed Bayes factor is examined by numerical studies. The second project deals with the intrinsic Bayesian inference for the correlation coefficient between the disturbances in the system of two seemingly unrelated regression equations. This work was inspired by the observation that considerable attention has been paid to the improved estimation of the regression coefficients of each model, whereas little attention has just been paid for making inference of the correlation coefficient, even though most of the improved estimation of the regression coefficients depend on the correlation coefficient. We propose an objective Bayesian solution to the problems of hypothesis testing and point estimation for the correlation coefficient based on combined use of the invariant loss function and the objective prior distribution for the unknown model parameters. This new solution possesses an invariance property under monotonic reparameterization of the quantity of interest. Some simulation studies and one real-data example are given for illustrative purpose. In the third project, we propose a new Bayesian strength of evidence built on divergence measures for testing point null hypotheses. Our proposed approach can be viewed as an objective and automatic approach to the problem of testing a point null hypothesis. It is shown that the new evidence successfully reconciles the disagreement between frequentists and Bayesians in many classical examples in which Lindley's paradox often occurs. In particular, note that the proposed Bayesian approach under the noninformative prior often recovers the frequentist P-values. From a Bayesian decision-theoretical viewpoint, it is justified that the new evidence is a formal Bayes test for some specific loss functions. The performance of the proposed approach is illustrated through several numerical examples. Possible applications of the new evidence for a variety of point null hypothesis testing problems are also briefly discussed.
Download or read book Model Selection written by Parhasarathi Lahiri and published by IMS. This book was released on 2001 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Variable Selection Based on Test Statistics written by Andrea Malaguerra and published by . This book was released on 2012 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Bayesian Variable Selection written by Mahlet G. Tadesse and published by CRC Press. This book was released on 2021-12-24 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed. The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions. Features: Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material
Download or read book Bayesian Statistics 9 written by José M. Bernardo and published by Oxford University Press. This book was released on 2011-10-06 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian statistics is a dynamic and fast-growing area of statistical research and the Valencia International Meetings provide the main forum for discussion. These resulting proceedings form an up-to-date collection of research.
Download or read book A First Course in Linear Model Theory written by Nalini Ravishanker and published by CRC Press. This book was released on 2001-12-21 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear models A First Course in Linear Model Theory systematically presents the basic theory behind linear statistical models with motivation from an algebraic as well as a geometric perspective. Through the concepts and tools of matrix and linear algebra and distribution theory, it provides a framework for understanding classical and contemporary linear model theory. It does not merely introduce formulas, but develops in students the art of statistical thinking and inspires learning at an intuitive level by emphasizing conceptual understanding. The authors' fresh approach, methodical presentation, wealth of examples, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.
Download or read book Informative Hypotheses written by Herbert Hoijtink and published by CRC Press. This book was released on 2011-10-26 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: When scientists formulate their theories, expectations, and hypotheses, they often use statements like: ``I expect mean A to be bigger than means B and C"; ``I expect that the relation between Y and both X1 and X2 is positive"; and ``I expect the relation between Y and X1 to be stronger than the relation between Y and X2". Stated otherwise, they formulate their expectations in terms of inequality constraints among the parameters in which they are interested, that is, they formulate Informative Hypotheses. There is currently a sound theoretical foundation for the evaluation of informative hypotheses using Bayes factors, p-values and the generalized order restricted information criterion. Furthermore, software that is often free is available to enable researchers to evaluate the informative hypotheses using their own data. The road is open to challenge the dominance of the null hypothesis for contemporary research in behavioral, social, and other sciences.
Download or read book Bayesian Evaluation of Informative Hypotheses written by Herbert Hoijtink and published by Springer Science & Business Media. This book was released on 2008-09-08 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the developments in the area of Bayesian evaluation of informative hypotheses that took place since the publication of the ?rst paper on this topic in 2001 [Hoijtink, H. Con?rmatory latent class analysis, model selection using Bayes factors and (pseudo) likelihood ratio statistics. Multivariate Behavioral Research, 36, 563–588]. The current state of a?airs was presented and discussed by the authors of this book during a workshop in Utrecht in June 2007. Here we would like to thank all authors for their participation, ideas, and contributions. We would also like to thank Sophie van der Zee for her editorial e?orts during the construction of this book. Another word of thanks is due to John Kimmel of Springer for his con?dence in the editors and authors. Finally, we would like to thank the Netherlands Organization for Scienti?c Research (NWO) whose VICI grant (453-05-002) awarded to the ?rst author enabled the organization of the workshop, the writing of this book, and continuation of the research with respect to Bayesian evaluation of informative hypotheses.
Download or read book Hypothesis Testing and Model Selection in the Social Sciences written by David L. Weakliem and published by Guilford Publications. This book was released on 2016-04-25 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examining the major approaches to hypothesis testing and model selection, this book blends statistical theory with recommendations for practice, illustrated with real-world social science examples. It systematically compares classical (frequentist) and Bayesian approaches, showing how they are applied, exploring ways to reconcile the differences between them, and evaluating key controversies and criticisms. The book also addresses the role of hypothesis testing in the evaluation of theories, the relationship between hypothesis tests and confidence intervals, and the role of prior knowledge in Bayesian estimation and Bayesian hypothesis testing. Two easily calculated alternatives to standard hypothesis tests are discussed in depth: the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The companion website ([ital]www.guilford.com/weakliem-materials[/ital]) supplies data and syntax files for the book's examples.
Download or read book Learning Statistics with R written by Daniel Navarro and published by Lulu.com. This book was released on 2013-01-13 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Learning Statistics with R" covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software and adopting a light, conversational style throughout. The book discusses how to get started in R, and gives an introduction to data manipulation and writing scripts. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, t-tests, ANOVAs and regression. Bayesian statistics are covered at the end of the book. For more information (and the opportunity to check the book out before you buy!) visit http://ua.edu.au/ccs/teaching/lsr or http://learningstatisticswithr.com
Download or read book Bayesian Variable Selection for High Dimensional Data Analysis written by Yang Aijun and published by LAP Lambert Academic Publishing. This book was released on 2011-09 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the practice of statistical modeling, it is often desirable to have an accurate predictive model. Modern data sets usually have a large number of predictors.Hence parsimony is especially an important issue. Best-subset selection is a conventional method of variable selection. Due to the large number of variables with relatively small sample size and severe collinearity among the variables, standard statistical methods for selecting relevant variables often face difficulties. Bayesian stochastic search variable selection has gained much empirical success in a variety of applications. This book, therefore, proposes a modified Bayesian stochastic variable selection approach for variable selection and two/multi-class classification based on a (multinomial) probit regression model.We demonstrate the performance of the approach via many real data. The results show that our approach selects smaller numbers of relevant variables and obtains competitive classification accuracy based on obtained results.
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 Bayesian Modeling Using WinBUGS written by Ioannis Ntzoufras and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A hands-on introduction to the principles of Bayesian modeling using WinBUGS Bayesian Modeling Using WinBUGS provides an easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling settings. The author provides an accessible treatment of the topic, offering readers a smooth introduction to the principles of Bayesian modeling with detailed guidance on the practical implementation of key principles. The book begins with a basic introduction to Bayesian inference and the WinBUGS software and goes on to cover key topics, including: Markov Chain Monte Carlo algorithms in Bayesian inference Generalized linear models Bayesian hierarchical models Predictive distribution and model checking Bayesian model and variable evaluation Computational notes and screen captures illustrate the use of both WinBUGS as well as R software to apply the discussed techniques. Exercises at the end of each chapter allow readers to test their understanding of the presented concepts and all data sets and code are available on the book's related Web site. Requiring only a working knowledge of probability theory and statistics, Bayesian Modeling Using WinBUGS serves as an excellent book for courses on Bayesian statistics at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners in the fields of statistics, actuarial science, medicine, and the social sciences who use WinBUGS in their everyday work.
Download or read book Jointness in Bayesian Variable Selection with Applications to Growth Regression written by and published by World Bank Publications. This book was released on with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Multiplicity Adjustment in Bayesian Variable Selection and an Objective Bayesian Analysis of a Crossover Design written by Dandan Li and published by . This book was released on 2014 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiplicity is a common problem in multiple testing for both traditional and Bayesian approaches. The first part of this dissertation considers certain issues relating to multiplicity adjustment in the Bayesian approach. Scott and Berger (2010) explained how multiplicity adjustment is achieved in fully Bayesian approach for model selection by using a single prior on inclusion probability in terms of model prior odds ratio. We extend their work by studying the general properties of model prior odds ratio and using it to propose a measure to quantify the multiplicity adjustment induced by a prior in fully Bayesian framework. Simulation studies are performed to evaluate the proposed measure. Estimation and testing hypotheses about the treatment effects in a crossover design is interesting as it involves consideration whether the carryover effect is present or not. Presence or absence of carryover effect also may depend on the existence of treatment effect. In the second part of this dissertation, we consider a crossover design with normally distributed response variable, and use standard objective priors for estimation and model selection to estimate the treatment effect, and test hypothesis about it. The performance is evaluated by simulation studies through MSE and coverage probability of confidence interval. We apply the approach to a real data example and compare the numerical results with other frequentist and Bayesian approaches.
