Download or read book A Bayesian Framework for Multimodel Regression written by Timothy DelSole and published by . This book was released on 2006 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Multilevel Models for Repeated Measures Data written by Santiago Barreda and published by Taylor & Francis. This book was released on 2023-05-18 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive book is an introduction to multilevel Bayesian models in R using brms and the Stan programming language. Featuring a series of fully worked analyses of repeated measures data, the focus is placed on active learning through the analyses of the progressively more complicated models presented throughout the book. In this book, the authors offer an introduction to statistics entirely focused on repeated measures data beginning with very simple two-group comparisons and ending with multinomial regression models with many ‘random effects’. Across 13 well-structured chapters, readers are provided with all the code necessary to run all the analyses and make all the plots in the book, as well as useful examples of how to interpret and write up their own analyses. This book provides an accessible introduction for readers in any field, with any level of statistical background. Senior undergraduate students, graduate students, and experienced researchers looking to ‘translate’ their skills with more traditional models to a Bayesian framework will benefit greatly from the lessons in this text.
Download or read book Model Selection and Multimodel Inference written by Kenneth P. Burnham and published by Springer Science & Business Media. This book was released on 2007-05-28 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique and comprehensive text on the philosophy of model-based data analysis and strategy for the analysis of empirical data. The book introduces information theoretic approaches and focuses critical attention on a priori modeling and the selection of a good approximating model that best represents the inference supported by the data. It contains several new approaches to estimating model selection uncertainty and incorporating selection uncertainty into estimates of precision. An array of examples is given to illustrate various technical issues. The text has been written for biologists and statisticians using models for making inferences from empirical data.
Download or read book Bayesian Regression Modeling with INLA written by Xiaofeng Wang and published by CRC Press. This book was released on 2018-01-29 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: INLA stands for Integrated Nested Laplace Approximations, which is a new method for fitting a broad class of Bayesian regression models. No samples of the posterior marginal distributions need to be drawn using INLA, so it is a computationally convenient alternative to Markov chain Monte Carlo (MCMC), the standard tool for Bayesian inference. Bayesian Regression Modeling with INLA covers a wide range of modern regression models and focuses on the INLA technique for building Bayesian models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to demonstrate the interplay of theory and practice with reproducible studies. Complete R commands are provided for each example, and a supporting website holds all of the data described in the book. An R package including the data and additional functions in the book is available to download. The book is aimed at readers who have a basic knowledge of statistical theory and Bayesian methodology. It gets readers up to date on the latest in Bayesian inference using INLA and prepares them for sophisticated, real-world work. Xiaofeng Wang is Professor of Medicine and Biostatistics at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and a Full Staff in the Department of Quantitative Health Sciences at Cleveland Clinic. Yu Ryan Yue is Associate Professor of Statistics in the Paul H. Chook Department of Information Systems and Statistics at Baruch College, The City University of New York. Julian J. Faraway is Professor of Statistics in the Department of Mathematical Sciences at the University of Bath.
Download or read book Model Averaging written by David Fletcher and published by Springer. This book was released on 2019-01-17 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise and accessible overview of model averaging, with a focus on applications. Model averaging is a common means of allowing for model uncertainty when analysing data, and has been used in a wide range of application areas, such as ecology, econometrics, meteorology and pharmacology. The book presents an overview of the methods developed in this area, illustrating many of them with examples from the life sciences involving real-world data. It also includes an extensive list of references and suggestions for further research. Further, it clearly demonstrates the links between the methods developed in statistics, econometrics and machine learning, as well as the connection between the Bayesian and frequentist approaches to model averaging. The book appeals to statisticians and scientists interested in what methods are available, how they differ and what is known about their properties. It is assumed that readers are familiar with the basic concepts of statistical theory and modelling, including probability, likelihood and generalized linear models.
Download or read book Bayesian Data Analysis in Ecology Using Linear Models with R BUGS and Stan written by Franzi Korner-Nievergelt and published by Academic Press. This book was released on 2015-04-04 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and STAN examines the Bayesian and frequentist methods of conducting data analyses. The book provides the theoretical background in an easy-to-understand approach, encouraging readers to examine the processes that generated their data. Including discussions of model selection, model checking, and multi-model inference, the book also uses effect plots that allow a natural interpretation of data. Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and STAN introduces Bayesian software, using R for the simple modes, and flexible Bayesian software (BUGS and Stan) for the more complicated ones. Guiding the ready from easy toward more complex (real) data analyses ina step-by-step manner, the book presents problems and solutions—including all R codes—that are most often applicable to other data and questions, making it an invaluable resource for analyzing a variety of data types. - Introduces Bayesian data analysis, allowing users to obtain uncertainty measurements easily for any derived parameter of interest - Written in a step-by-step approach that allows for eased understanding by non-statisticians - Includes a companion website containing R-code to help users conduct Bayesian data analyses on their own data - All example data as well as additional functions are provided in the R-package blmeco
Download or read book Probability and Bayesian Modeling written by Jim Albert and published by CRC Press. This book was released on 2019-12-06 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.
Download or read book Bayesian Model Selection Consistency for High dimensional Regression written by Min Hua and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian model selection has enjoyed considerable prominence in high-dimensional variable selection in recent years. Despite its popularity, the asymptotic theory for high-dimensional variable selection has not been fully explored yet. In this study, we aim to identify prior conditions for Bayesian model selection consistency under high-dimensional regression settings. In a Bayesian framework, posterior model probabilities can be used to quantify the importance of models given the observed data. Hence, our focus is on the asymptotic behavior of posterior model probabilities when the number of the potential predictors grows with the sample size. This dissertation contains the following three projects. In the first project, we investigate the asymptotic behavior of posterior model probabilities under the Zellner's g-prior, which is one of the most popular choices for model selection in Bayesian linear regression. We establish a simple and intuitive condition of the Zellner's g-prior under which the posterior model distribution tends to be concentrated at the true model as the sample size increases even if the number of predictors grows much faster than the sample size does. Simulation study results indicate that the satisfaction of our condition is essential for the success of Bayesian high-dimensional variable selection under the g-prior. In the second project, we extend our framework to a general class of priors. The most pressing challenge in our generalization is that the marginal likelihood cannot be expressed in a closed form. To address this problem, we develop a general form of Laplace approximation under a high-dimensional setting. As a result, we establish general sufficient conditions for high-dimensional Bayesian model selection consistency. Our simulation study and real data analysis demonstrate that the proposed condition allows us to identify the true data generating model consistently. In the last project, we extend our framework to Bayesian generalized linear regression models. The distinctive feature of our proposed framework is that we do not impose any specific form of data distribution. In this project we develop a general condition under which the true model tends to maximize the marginal likelihood even when the number of predictors increases faster than the sample size. Our condition provides useful guidelines for the specification of priors including hyperparameter selection. Our simulation study demonstrates the validity of the proposed condition for Bayesian model selection consistency with non-Gaussian data.
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 Bringing Bayesian Models to Life written by Mevin B. Hooten and published by CRC Press. This book was released on 2019-05-15 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing Bayesian Models to Life empowers the reader to extend, enhance, and implement statistical models for ecological and environmental data analysis. We open the black box and show the reader how to connect modern statistical models to computer algorithms. These algorithms allow the user to fit models that answer their scientific questions without needing to rely on automated Bayesian software. We show how to handcraft statistical models that are useful in ecological and environmental science including: linear and generalized linear models, spatial and time series models, occupancy and capture-recapture models, animal movement models, spatio-temporal models, and integrated population-models. Features: R code implementing algorithms to fit Bayesian models using real and simulated data examples. A comprehensive review of statistical models commonly used in ecological and environmental science. Overview of Bayesian computational methods such as importance sampling, MCMC, and HMC. Derivations of the necessary components to construct statistical algorithms from scratch. Bringing Bayesian Models to Life contains a comprehensive treatment of models and associated algorithms for fitting the models to data. We provide detailed and annotated R code in each chapter and apply it to fit each model we present to either real or simulated data for instructional purposes. Our code shows how to create every result and figure in the book so that readers can use and modify it for their own analyses. We provide all code and data in an organized set of directories available at the authors' websites.
Download or read book Bayesian Model Selection and Statistical Modeling written by Tomohiro Ando and published by CRC Press. This book was released on 2010-05-27 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with many practical applications, Bayesian Model Selection and Statistical Modeling presents an array of Bayesian inference and model selection procedures. It thoroughly explains the concepts, illustrates the derivations of various Bayesian model selection criteria through examples, and provides R code for implementation. The author shows how to implement a variety of Bayesian inference using R and sampling methods, such as Markov chain Monte Carlo. He covers the different types of simulation-based Bayesian model selection criteria, including the numerical calculation of Bayes factors, the Bayesian predictive information criterion, and the deviance information criterion. He also provides a theoretical basis for the analysis of these criteria. In addition, the author discusses how Bayesian model averaging can simultaneously treat both model and parameter uncertainties. Selecting and constructing the appropriate statistical model significantly affect the quality of results in decision making, forecasting, stochastic structure explorations, and other problems. Helping you choose the right Bayesian model, this book focuses on the framework for Bayesian model selection and includes practical examples of model selection criteria.
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 Regression Modelling wih Spatial and Spatial Temporal Data written by Robert P. Haining and published by CRC Press. This book was released on 2020-01-27 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling Spatial and Spatial-Temporal Data: A Bayesian Approach is aimed at statisticians and quantitative social, economic and public health students and researchers who work with spatial and spatial-temporal data. It assumes a grounding in statistical theory up to the standard linear regression model. The book compares both hierarchical and spatial econometric modelling, providing both a reference and a teaching text with exercises in each chapter. The book provides a fully Bayesian, self-contained, treatment of the underlying statistical theory, with chapters dedicated to substantive applications. The book includes WinBUGS code and R code and all datasets are available online. Part I covers fundamental issues arising when modelling spatial and spatial-temporal data. Part II focuses on modelling cross-sectional spatial data and begins by describing exploratory methods that help guide the modelling process. There are then two theoretical chapters on Bayesian models and a chapter of applications. Two chapters follow on spatial econometric modelling, one describing different models, the other substantive applications. Part III discusses modelling spatial-temporal data, first introducing models for time series data. Exploratory methods for detecting different types of space-time interaction are presented followed by two chapters on the theory of space-time separable (without space-time interaction) and inseparable (with space-time interaction) models. An applications chapter includes: the evaluation of a policy intervention; analysing the temporal dynamics of crime hotspots; chronic disease surveillance; and testing for evidence of spatial spillovers in the spread of an infectious disease. A final chapter suggests some future directions and challenges.
Download or read book Bayesian Forecasting and Dynamic Models written by Mike West and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we are concerned with Bayesian learning and forecast ing in dynamic environments. We describe the structure and theory of classes of dynamic models, and their uses in Bayesian forecasting. The principles, models and methods of Bayesian forecasting have been developed extensively during the last twenty years. This devel opment has involved thorough investigation of mathematical and sta tistical aspects of forecasting models and related techniques. With this has come experience with application in a variety of areas in commercial and industrial, scientific and socio-economic fields. In deed much of the technical development has been driven by the needs of forecasting practitioners. As a result, there now exists a relatively complete statistical and mathematical framework, although much of this is either not properly documented or not easily accessible. Our primary goals in writing this book have been to present our view of this approach to modelling and forecasting, and to provide a rea sonably complete text for advanced university students and research workers. The text is primarily intended for advanced undergraduate and postgraduate students in statistics and mathematics. In line with this objective we present thorough discussion of mathematical and statistical features of Bayesian analyses of dynamic models, with illustrations, examples and exercises in each Chapter.
Download or read book Large Scale Machine Learning in the Earth Sciences written by Ashok N. Srivastava and published by CRC Press. This book was released on 2017-08-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Foreword: "While large-scale machine learning and data mining have greatly impacted a range of commercial applications, their use in the field of Earth sciences is still in the early stages. This book, edited by Ashok Srivastava, Ramakrishna Nemani, and Karsten Steinhaeuser, serves as an outstanding resource for anyone interested in the opportunities and challenges for the machine learning community in analyzing these data sets to answer questions of urgent societal interest...I hope that this book will inspire more computer scientists to focus on environmental applications, and Earth scientists to seek collaborations with researchers in machine learning and data mining to advance the frontiers in Earth sciences." --Vipin Kumar, University of Minnesota Large-Scale Machine Learning in the Earth Sciences provides researchers and practitioners with a broad overview of some of the key challenges in the intersection of Earth science, computer science, statistics, and related fields. It explores a wide range of topics and provides a compilation of recent research in the application of machine learning in the field of Earth Science. Making predictions based on observational data is a theme of the book, and the book includes chapters on the use of network science to understand and discover teleconnections in extreme climate and weather events, as well as using structured estimation in high dimensions. The use of ensemble machine learning models to combine predictions of global climate models using information from spatial and temporal patterns is also explored. The second part of the book features a discussion on statistical downscaling in climate with state-of-the-art scalable machine learning, as well as an overview of methods to understand and predict the proliferation of biological species due to changes in environmental conditions. The problem of using large-scale machine learning to study the formation of tornadoes is also explored in depth. The last part of the book covers the use of deep learning algorithms to classify images that have very high resolution, as well as the unmixing of spectral signals in remote sensing images of land cover. The authors also apply long-tail distributions to geoscience resources, in the final chapter of the book.
Download or read book A Bayesian Framework for Fully Nonparametric Ordinal Regression written by Maria Noel DeYoreo and published by . This book was released on 2014 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditional approaches to ordinal regression rely on strong parametric assumptions for the regression function and/or the underlying response distribution. While they simplify inference, restrictions such as normality and linearity are inappropriate for most settings, and the need for flexible, nonlinear models which relax common distributional assumptions is clear. Through the use of Bayesian nonparametric modeling techniques, nonstandard features of regression relationships may be obtained if the data suggest them to be present. We introduce a general framework for multivariate ordinal regression, which is not restricted by linearity or additivity assumptions in the covariate effects. In particular, we assume the ordinal responses arise from latent continuous random variables through discretization, and model the latent response-covariate distribution using a Dirichlet process mixture of multivariate normals. We begin with the binary regression setting, both due to its prominent role in the literature and because it requires more specialized model development under our framework. In particular, we use a square-root-free Cholesky decomposition of the normal kernel covariance matrix, which facilitates model identifiability while allowing for appropriate dependence structure. Moreover, this model structure has the computational advantage of simplifying the implementation of Markov Chain Monte Carlo posterior simulation. Next, we develop modeling and inference methods for ordinal regression, including the underdeveloped setting that involves multivariate ordinal responses. Standard parametric models for ordinal regression suffer from computational challenges arising from identifiability constraints and parameter estimation, whereas due to the flexible nature of the nonparametric model, we overcome these difficulties. The modeling approach is further developed to handle ordinal regressions which are indexed in discrete-time, through use of a dependent Dirichlet process prior, which estimates the unique regression relationship at each time point in a flexible way while incorporating dependence across time. We consider several examples involving synthetic data to study the scope of the proposed methodology with respect to inference and prediction under both standard and more complex scenarios for the underlying data generating mechanism. Moreover, a variety of real data examples are used to illustrate our methods. As this methodology is especially well-suited to problems in ecology and population dynamics, we target applications in these areas. In particular, our methods are used to provide a detailed analysis of a data set on rockfish maturity and body characteristics collected across different years.
Download or read book Learning Bayesian Models with R written by Dr. Hari M. Koduvely and published by Packt Publishing Ltd. This book was released on 2015-10-28 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Become an expert in Bayesian Machine Learning methods using R and apply them to solve real-world big data problems About This Book Understand the principles of Bayesian Inference with less mathematical equations Learn state-of-the art Machine Learning methods Familiarize yourself with the recent advances in Deep Learning and Big Data frameworks with this step-by-step guide Who This Book Is For This book is for statisticians, analysts, and data scientists who want to build a Bayes-based system with R and implement it in their day-to-day models and projects. It is mainly intended for Data Scientists and Software Engineers who are involved in the development of Advanced Analytics applications. To understand this book, it would be useful if you have basic knowledge of probability theory and analytics and some familiarity with the programming language R. What You Will Learn Set up the R environment Create a classification model to predict and explore discrete variables Get acquainted with Probability Theory to analyze random events Build Linear Regression models Use Bayesian networks to infer the probability distribution of decision variables in a problem Model a problem using Bayesian Linear Regression approach with the R package BLR Use Bayesian Logistic Regression model to classify numerical data Perform Bayesian Inference on massively large data sets using the MapReduce programs in R and Cloud computing In Detail Bayesian Inference provides a unified framework to deal with all sorts of uncertainties when learning patterns form data using machine learning models and use it for predicting future observations. However, learning and implementing Bayesian models is not easy for data science practitioners due to the level of mathematical treatment involved. Also, applying Bayesian methods to real-world problems requires high computational resources. With the recent advances in computation and several open sources packages available in R, Bayesian modeling has become more feasible to use for practical applications today. Therefore, it would be advantageous for all data scientists and engineers to understand Bayesian methods and apply them in their projects to achieve better results. Learning Bayesian Models with R starts by giving you a comprehensive coverage of the Bayesian Machine Learning models and the R packages that implement them. It begins with an introduction to the fundamentals of probability theory and R programming for those who are new to the subject. Then the book covers some of the important machine learning methods, both supervised and unsupervised learning, implemented using Bayesian Inference and R. Every chapter begins with a theoretical description of the method explained in a very simple manner. Then, relevant R packages are discussed and some illustrations using data sets from the UCI Machine Learning repository are given. Each chapter ends with some simple exercises for you to get hands-on experience of the concepts and R packages discussed in the chapter. The last chapters are devoted to the latest development in the field, specifically Deep Learning, which uses a class of Neural Network models that are currently at the frontier of Artificial Intelligence. The book concludes with the application of Bayesian methods on Big Data using the Hadoop and Spark frameworks. Style and approach The book first gives you a theoretical description of the Bayesian models in simple language, followed by details of its implementation in the R package. Each chapter has illustrations for the use of Bayesian model and the corresponding R package, using data sets from the UCI Machine Learning repository. Each chapter also contains sufficient exercises for you to get more hands-on practice.
