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Bayesian Variable Selection In Regression With Genetics Application
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Book Synopsis Bayesian Variable Selection in Regression with Genetics Application by : Zayed Shahjahan
Download or read book Bayesian Variable Selection in Regression with Genetics Application written by Zayed Shahjahan and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this project, we consider a simple new approach to variable selection in linear regression based on the Sum-of-Single-Effects model. The approach is particularly well-suited to big-data settings where variables are highly correlated and effects are sparse. The approach shares the computational simplicity and speed of traditional stepwise methods of variable selection in regression, but instead of selecting a single variable at each step, computes a distribution on variables that captures uncertainty in which variable to select. This uncertainty in variable selection is summarized conveniently by credible sets of variables with an attached probability for the entire set. To illustrate the approach, we apply it to a big-data problem in genetics.
Book Synopsis Handbook of Bayesian Variable Selection by : Mahlet G. Tadesse
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 491 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
Book Synopsis Jointness in Bayesian Variable Selection with Applications to Growth Regression by :
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:
Book Synopsis Bayesian Variable Selection in Linear and Non-linear Models by : Arnab Kumar Maity
Download or read book Bayesian Variable Selection in Linear and Non-linear Models written by Arnab Kumar Maity and published by . This book was released on 2016 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Appropriate feature selection is a fundamental problem in the field of statistics. Models with large number of features or variables require special attention due to the computational complexity of the huge model space. This is generally known as the variable or model selection problem in the field of statistics whereas in machine learning and other literature, this is also known as feature selection, attribute selection or variable subset selection. The method of variable selection is the process of efficiently selecting an optimal subset of relevant variables for use in model construction. The central assumption in this methodology is that the data contain many redundant variable; those which do not provide any significant additional information than the optimally selected subset of variable. Variable selection is widely used in all application areas of data analytics, ranging from optimal selection of genes in large scale micro-array studies, to optimal selection of biomarkers for targeted therapy in cancer genomics to selection of optimal predictors in business analytics. Under the Bayesian approach, the formal way to perform this optimal selection is to select the model with highest posterior probability. Using this fact the problem may be thought as an optimization problem over the model space where the objective function is the posterior probability of model and the maximization is taken place with respect to the models. We propose an efficient method for implementing this optimization and we illustrate its feasibility in high dimensional problems. By means of various simulation studies, this new approach has been shown to be efficient and to outperform other statistical feature selection methods methods namely median probability model and sampling method with frequency based estimators. Theoretical justifications are provided. Applications to logistic regression and survival regression are discussed.
Book Synopsis Genome-Wide Association Studies and Genomic Prediction by : Cedric Gondro
Download or read book Genome-Wide Association Studies and Genomic Prediction written by Cedric Gondro and published by Humana Press. This book was released on 2013-06-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the detailed genomic information that is now becoming available, we have a plethora of data that allows researchers to address questions in a variety of areas. Genome-wide association studies (GWAS) have become a vital approach to identify candidate regions associated with complex diseases in human medicine, production traits in agriculture, and variation in wild populations. Genomic prediction goes a step further, attempting to predict phenotypic variation in these traits from genomic information. Genome-Wide Association Studies and Genomic Prediction pulls together expert contributions to address this important area of study. The volume begins with a section covering the phenotypes of interest as well as design issues for GWAS, then moves on to discuss efficient computational methods to store and handle large datasets, quality control measures, phasing, haplotype inference, and imputation. Later chapters deal with statistical approaches to data analysis where the experimental objective is either to confirm the biology by identifying genomic regions associated to a trait or to use the data to make genomic predictions about a future phenotypic outcome (e.g. predict onset of disease). As part of the Methods in Molecular Biology series, chapters provide helpful, real-world implementation advice.
Book Synopsis Advanced Mean Field Methods by : Manfred Opper
Download or read book Advanced Mean Field Methods written by Manfred Opper and published by MIT Press. This book was released on 2001 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling. A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.
Book Synopsis Jointness in Bayesian Variable Selection with Applications to Growth Regression by : Eduardo Ley
Download or read book Jointness in Bayesian Variable Selection with Applications to Growth Regression written by Eduardo Ley and published by . This book was released on 2016 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present a measure of jointness to explore dependence among regressors in the context of Bayesian model selection. The jointness measure they propose equals the posterior odds ratio between those models that include a set of variables and the models that only include proper subsets. They show its application in cross-country growth regressions using two data-sets from the model-averaging growth literature.
Book Synopsis Multivariate Statistical Machine Learning Methods for Genomic Prediction by : Osval Antonio Montesinos López
Download or read book Multivariate Statistical Machine Learning Methods for Genomic Prediction written by Osval Antonio Montesinos López and published by Springer Nature. This book was released on 2022-02-14 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension.The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool.
Book Synopsis Application of Bayesian Hierarchical Models in Genetic Data Analysis by : Lin Zhang
Download or read book Application of Bayesian Hierarchical Models in Genetic Data Analysis written by Lin Zhang and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Genetic data analysis has been capturing a lot of attentions for understanding the mechanism of the development and progressing of diseases like cancers, and is crucial in discovering genetic markers and treatment targets in medical research. This dissertation focuses on several important issues in genetic data analysis, graphical network modeling, feature selection, and covariance estimation. First, we develop a gene network modeling method for discrete gene expression data, produced by technologies such as serial analysis of gene expression and RNA sequencing experiment, which generate counts of mRNA transcripts in cell samples. We propose a generalized linear model to fit the discrete gene expression data and assume that the log ratios of the mean expression levels follow a Gaussian distribution. We derive the gene network structures by selecting covariance matrices of the Gaussian distribution with a hyper-inverse Wishart prior. We incorporate prior network models based on Gene Ontology information, which avails existing biological information on the genes of interest. Next, we consider a variable selection problem, where the variables have natural grouping structures, with application to analysis of chromosomal copy number data. The chromosomal copy number data are produced by molecular inversion probes experiments which measure probe-specific copy number changes. We propose a novel Bayesian variable selection method, the hierarchical structured variable se- lection (HSVS) method, which accounts for the natural gene and probe-within-gene architecture to identify important genes and probes associated with clinically relevant outcomes. We propose the HSVS model for grouped variable selection, where simultaneous selection of both groups and within-group variables is of interest. The HSVS model utilizes a discrete mixture prior distribution for group selection and group-specific Bayesian lasso hierarchies for variable selection within groups. We further provide methods for accounting for serial correlations within groups that incorporate Bayesian fused lasso methods for within-group selection. Finally, we propose a Bayesian method of estimating high-dimensional covariance matrices that can be decomposed into a low rank and sparse component. This covariance structure has a wide range of applications including factor analytical model and random effects model. We model the covariance matrices with the decomposition structure by representing the covariance model in the form of a factor analytic model where the number of latent factors is unknown. We introduce binary indicators for estimating the rank of the low rank component combined with a Bayesian graphical lasso method for estimating the sparse component. We further extend our method to a graphical factor analytic model where the graphical model of the residuals is of interest. We achieve sparse estimation of the inverse covariance of the residuals in the graphical factor model by employing a hyper-inverse Wishart prior method for a decomposable graph and a Bayesian graphical lasso method for an unrestricted graph. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148056
Book Synopsis Bayesian Variable Selection for Time Series Regression, with Application to Waste Water Monitoring by : Ian Roddis
Download or read book Bayesian Variable Selection for Time Series Regression, with Application to Waste Water Monitoring written by Ian Roddis and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variable Selection Via Penalized Regression and the Genetic Algorithm Using Information Complexity, with Applications for High-dimensional -omics Data by : Tyler J. Massaro
Download or read book Variable Selection Via Penalized Regression and the Genetic Algorithm Using Information Complexity, with Applications for High-dimensional -omics Data written by Tyler J. Massaro and published by . This book was released on 2016 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is a collection of examples, algorithms, and techniques for researchers interested in selecting influential variables from statistical regression models. Chapters 1, 2, and 3 provide background information that will be used throughout the remaining chapters, on topics including but not limited to information complexity, model selection, covariance estimation, stepwise variable selection, penalized regression, and especially the genetic algorithm (GA) approach to variable subsetting. In chapter 4, we fully develop the framework for performing GA subset selection in logistic regression models. We present advantages of this approach against stepwise and elastic net regularized regression in selecting variables from a classical set of ICU data. We further compare these results to an entirely new procedure for variable selection developed explicitly for this dissertation, called the post hoc adjustment of measured effects (PHAME). In chapter 5, we reproduce many of the same results from chapter 4 for the first time in a multinomial logistic regression setting. The utility and convenience of the PHAME procedure is demonstrated on a set of cancer genomic data. Chapter 6 marks a departure from supervised learning problems as we shift our focus to unsupervised problems involving mixture distributions of count data from epidemiologic fields. We start off by reintroducing Minimum Hellinger Distance estimation alongside model selection techniques as a worthy alternative to the EM algorithm for generating mixtures of Poisson distributions. We also create for the first time a GA that derives mixtures of negative binomial distributions. The work from chapter 6 is incorporated into chapters 7 and 8, where we conclude the dissertation with a novel analysis of mixtures of count data regression models. We provide algorithms based on single and multi-target genetic algorithms which solve the mixture of penalized count data regression models problem, and we demonstrate the usefulness of this technique on HIV count data that were used in a previous study published by Gray, Massaro et al. (2015) as well as on time-to-event data taken from the cancer genomic data sets from earlier.
Book Synopsis Application of Bayesian Variable Selection in Two Sociological Data Sets by : Suhai Liu
Download or read book Application of Bayesian Variable Selection in Two Sociological Data Sets written by Suhai Liu and published by . This book was released on 1998 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robust Bayesian Variable Selection in Finite Mixture Regression Model with an Application to Financial Crisis Data by :
Download or read book Robust Bayesian Variable Selection in Finite Mixture Regression Model with an Application to Financial Crisis Data written by and published by . This book was released on 2015 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonparametric Regression Using Bayesian Variable Selection by : Michael Smith
Download or read book Nonparametric Regression Using Bayesian Variable Selection written by Michael Smith and published by . This book was released on 1994 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis High-dimensional Variable Selection for Genomics Data, from Both Frequentist and Bayesian Perspectives by : Jie Ren
Download or read book High-dimensional Variable Selection for Genomics Data, from Both Frequentist and Bayesian Perspectives written by Jie Ren and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Variable selection is one of the most popular tools for analyzing high-dimensional genomic data. It has been developed to accommodate complex data structures and lead to structured sparse identification of important genomics features. We focus on the network and interaction structure that commonly exist in genomic data, and develop novel variable selection methods from both frequentist and Bayesian perspectives. Network-based regularization has achieved success in variable selections for high-dimensional cancer genomic data, due to its ability to incorporate the correlations among genomic features. However, as survival time data usually follow skewed distributions, and are contaminated by outliers, network-constrained regularization that does not take the robustness into account leads to false identifications of network structure and biased estimation of patients' survival. In the first project, we develop a novel robust network-based variable selection method under the accelerated failure time (AFT) model. Extensive simulation studies show the advantage of the proposed method over the alternative methods. Promising findings are made in two case studies of lung cancer datasets with high dimensional gene expression measurements. Gene-environment (G×E) interactions are important for the elucidation of disease etiology beyond the main genetic and environmental effects. In the second project, a novel and powerful semi-parametric Bayesian variable selection model has been proposed to investigate linear and nonlinear G×E interactions simultaneously. It can further conduct structural identification by distinguishing nonlinear interactions from main-effects-only case within the Bayesian framework. The proposed method conducts Bayesian variable selection more efficiently and accurately than alternatives. Simulation shows that the proposed model outperforms competing alternatives in terms of both identification and prediction. In the case study, the proposed Bayesian method leads to the identification of effects with important implications in a high-throughput profiling study with high-dimensional SNP data. In the last project, a robust Bayesian variable selection method has been developed for G×E interaction studies. The proposed robust Bayesian method can effectively accommodate heavy-tailed errors and outliers in the response variable while conducting variable selection by accounting for structural sparsity. Spike and slab priors are incorporated on both individual and group levels to identify the sparse main and interaction effects. Extensive simulation studies and analysis of both the diabetes data with SNP measurements from the Nurses' Health Study and TCGA melanoma data with gene expression measurements demonstrate the superior performance of the proposed method over multiple competing alternatives. To facilitate reproducible research and fast computation, we have developed open source R packages for each project, which provide highly efficient C++ implementation for all the proposed and alternative approaches. The R packages regnet and spinBayes, associated with the first and second project correspondingly, are available on CRAN. For the third project, the R package robin is available from GitHub and will be submitted to CRAN soon.
Book Synopsis Bayesian Analysis of Gene Expression Data by : Bani K. Mallick
Download or read book Bayesian Analysis of Gene Expression Data written by Bani K. Mallick and published by John Wiley & Sons. This book was released on 2009-07-20 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of high-throughput genetic experimentation is evolving rapidly, with the advent of new technologies and new venues for data mining. Bayesian methods play a role central to the future of data and knowledge integration in the field of Bioinformatics. This book is devoted exclusively to Bayesian methods of analysis for applications to high-throughput gene expression data, exploring the relevant methods that are changing Bioinformatics. Case studies, illustrating Bayesian analyses of public gene expression data, provide the backdrop for students to develop analytical skills, while the more experienced readers will find the review of advanced methods challenging and attainable. This book: Introduces the fundamentals in Bayesian methods of analysis for applications to high-throughput gene expression data. Provides an extensive review of Bayesian analysis and advanced topics for Bioinformatics, including examples that extensively detail the necessary applications. Accompanied by website featuring datasets, exercises and solutions. Bayesian Analysis of Gene Expression Data offers a unique introduction to both Bayesian analysis and gene expression, aimed at graduate students in Statistics, Biomedical Engineers, Computer Scientists, Biostatisticians, Statistical Geneticists, Computational Biologists, applied Mathematicians and Medical consultants working in genomics. Bioinformatics researchers from many fields will find much value in this book.
Book Synopsis Bayesian Variable Selection by : Zuofeng Shang
Download or read book Bayesian Variable Selection written by Zuofeng Shang and published by . This book was released on 2011 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
