Download or read book Fast Algorithms for Bayesian Variable Selection written by Xichen Huang and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Scalable Algorithms for Bayesian Variable Selection written by Jin Wang and published by . This book was released on 2016 with total page 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 Variable Selection and Functional Data Analysis written by Asish Kumar Banik and published by . This book was released on 2019 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-dimensional statistics is one of the most studied topics in the field of statistics. The most interesting problem to arise in the last 15 years is variable selection or subset selection. Variable selection is a strong statistical tool that can be explored in functional data analysis. In the first part of this thesis, we implement a Bayesian variable selection method for automatic knot selection. We propose a spike-and-slab prior on knots and formulate a conjugate stochastic search variable selection for significant knots. The computation is substantially faster than existing knot selection methods, as we use Metropolis-Hastings algorithms and a Gibbs sampler for estimation. This work focuses on a single nonlinear covariate, modeled as regression splines. In the next stage, we study Bayesian variable selection in additive models with high-dimensional predictors. The selection of nonlinear functions in models is highly important in recent research, and the Bayesian method of selection has more advantages than contemporary frequentist methods. Chapter 2 examines Bayesian sparse group lasso theory based on spike-and-slab priors to determine its applicability for variable selection and function estimation in nonparametric additive models.The primary objective of Chapter 3 is to build a classification method using longitudinal volumetric magnetic resonance imaging (MRI) data from five regions of interest (ROIs). A functional data analysis method is used to handle the longitudinal measurement of ROIs, and the functional coefficients are later used in the classification models. We propose a P\\'olya-gamma augmentation method to classify normal controls and diseased patients based on functional MRI measurements. We obtain fast-posterior sampling by avoiding the slow and complicated Metropolis-Hastings algorithm. Our main motivation is to determine the important ROIs that have the highest separating power to classify our dichotomous response. We compare the sensitivity, specificity, and accuracy of the classification based on single ROIs and with various combinations of them. We obtain a sensitivity of over 85% and a specificity of around 90% for most of the combinations.Next, we work with Bayesian classification and selection methodology. The main goal of Chapter 4 is to employ longitudinal trajectories in a significant number of sub-regional brain volumetric MRI data as statistical predictors for Alzheimer's disease (AD) classification. We use logistic regression in a Bayesian framework that includes many functional predictors. The direct sampling of regression coefficients from the Bayesian logistic model is difficult due to its complicated likelihood function. In high-dimensional scenarios, the selection of predictors is paramount with the introduction of either spike-and-slab priors, non-local priors, or Horseshoe priors. We seek to avoid the complicated Metropolis-Hastings approach and to develop an easily implementable Gibbs sampler. In addition, the Bayesian estimation provides proper estimates of the model parameters, which are also useful for building inference. Another advantage of working with logistic regression is that it calculates the log of odds of relative risk for AD compared to normal control based on the selected longitudinal predictors, rather than simply classifying patients based on cross-sectional estimates. Ultimately, however, we combine approaches and use a probability threshold to classify individual patients. We employ 49 functional predictors consisting of volumetric estimates of brain sub-regions, chosen for their established clinical significance. Moreover, the use of spike-and-slab priors ensures that many redundant predictors are dropped from the model.Finally, we present a new approach of Bayesian model-based clustering for spatiotemporal data in chapter 5 . A simple linear mixed model (LME) derived from a functional model is used to model spatiotemporal cerebral white matter data extracted from healthy aging individuals. LME provides us with prior information for spatial covariance structure and brain segmentation based on white matter intensity. This motivates us to build stochastic model-based clustering to group voxels considering their longitudinal and location information. The cluster-specific random effect causes correlation among repeated measures. The problem of finding partitions is dealt with by imposing prior structure on cluster partitions in order to derive a stochastic objective function.

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

Download or read book Bayesian Variable Selection for Logistic Models Using Auxiliary Mixture Sampling written by and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper presents an Markov Chain Monte Carlo algorithm for both variable and covariance selection in the context of logistic mixed effects models. This algorithm allows us to sample solely from standard densities, with no additional tuning being needed. We apply a stochastic search variable approach to select explanatory variables as well as to determine the structure of the random effects covariance matrix. For logistic mixed effects models prior determination of explanatory variables and random effects is no longer prerequisite since the definite structure is chosen in a data-driven manner in the course of the modeling procedure. As an illustration two real-data examples from finance and tourism studies are given. (author's abstract).

Download or read book Handbook of Graphs and Networks written by Stefan Bornholdt and published by John Wiley & Sons. This book was released on 2006-03-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex interacting networks are observed in systems from such diverse areas as physics, biology, economics, ecology, and computer science. For example, economic or social interactions often organize themselves in complex network structures. Similar phenomena are observed in traffic flow and in communication networks as the internet. In current problems of the Biosciences, prominent examples are protein networks in the living cell, as well as molecular networks in the genome. On larger scales one finds networks of cells as in neural networks, up to the scale of organisms in ecological food webs. This book defines the field of complex interacting networks in its infancy and presents the dynamics of networks and their structure as a key concept across disciplines. The contributions present common underlying principles of network dynamics and their theoretical description and are of interest to specialists as well as to the non-specialized reader looking for an introduction to this new exciting field. Theoretical concepts include modeling networks as dynamical systems with numerical methods and new graph theoretical methods, but also focus on networks that change their topology as in morphogenesis and self-organization. The authors offer concepts to model network structures and dynamics, focussing on approaches applicable across disciplines.

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 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 Statistical Learning with Sparsity written by Trevor Hastie and published by CRC Press. This book was released on 2015-05-07 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover New Methods for Dealing with High-Dimensional DataA sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underl

Download or read book Bayesian Variable Selection in Clustering Via Dirichlet Process Mixture Models written by Sinae Kim and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The increased collection of high-dimensional data in various fields has raised a strong interest in clustering algorithms and variable selection procedures. In this disserta- tion, I propose a model-based method that addresses the two problems simultane- ously. I use Dirichlet process mixture models to define the cluster structure and to introduce in the model a latent binary vector to identify discriminating variables. I update the variable selection index using a Metropolis algorithm and obtain inference on the cluster structure via a split-merge Markov chain Monte Carlo technique. I evaluate the method on simulated data and illustrate an application with a DNA microarray study. I also show that the methodology can be adapted to the problem of clustering functional high-dimensional data. There I employ wavelet thresholding methods in order to reduce the dimension of the data and to remove noise from the observed curves. I then apply variable selection and sample clustering methods in the wavelet domain. Thus my methodology is wavelet-based and aims at clustering the curves while identifying wavelet coefficients describing discriminating local features. I exemplify the method on high-dimensional and high-frequency tidal volume traces measured under an induced panic attack model in normal humans.

Download or read book Bayesian Variable Selection and Estimation written by Xiaofan Xu and published by . This book was released on 2014 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper considers the classical Bayesian variable selection problem and an important subproblem in which grouping information of predictors is available. We propose the Half Thresholding (HT) estimator for simultaneous variable selection and estimation with shrinkage priors. Under orthogonal design matrix, variable selection consistency and asymptotic distribution of HT estimators are investigated and the oracle property is established with Three Parameter Beta Mixture of Normals (TPBN) priors. We then revisit Bayesian group lasso and use spike and slab priors for variable selection at the group level. In the process, the connection of our model with penalized regression is demonstrated, and the role of posterior median for thresholding is pointed out. We show that the posterior median estimator has the oracle property for group variable selection and estimation under orthogonal design while the group lasso has suboptimal asymptotic estimation rate when variable selection consistency is achieved. Next we consider Bayesian sparse group lasso again with spike and slab priors to select variables both at the group level and also within the group, and develop the necessary algorithm for its implementation. We demonstrate via simulation that the posterior median estimator of our spike and slab models has excellent performance for both variable selection and estimation.

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.

Download or read book Advanced Methods in Bayesian Variable Selection and Causal Inference written by Can Cui and published by . This book was released on 2021 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bayesian Variable Selection written by Guiling Shi and published by . This book was released on 2017 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational Systems Bioinformatics written by Xiaobo Zhou and published by World Scientific. This book was released on 2008 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational systems biology is a new and rapidly developing field of research, concerned with understanding the structure and processes of biological systems at the molecular, cellular, tissue, and organ levels through computational modeling as well as novel information theoretic data and image analysis methods. By focusing on either information processing of biological data or on modeling physical and chemical processes of biosystems, and in combination with the recent breakthrough in deciphering the human genome, computational systems biology is guaranteed to play a central role in disease prediction and preventive medicine, gene technology and pharmaceuticals, and other biotechnology fields. This book begins by introducing the basic mathematical, statistical, and data mining principles of computational systems biology, and then presents bioinformatics technology in microarray and sequence analysis step-by-step. Offering an insightful look into the effectiveness of the systems approach in computational biology, it focuses on recurrent themes in bioinformatics, biomedical applications, and future directions for research.

Download or read book Bayesian Variable Selection and Post selection Inference written by Qiyiwen Zhang and published by . This book was released on 2020 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we first develop a novel perspective to compare Bayesian variable selection procedures in terms of their selection criteria as well as their finite-sample properties. Secondly, we investigate Bayesian post-selection inference in two types of selection problems: linear regression and population selection. We will demonstrate that both inference problems are susceptible to selection effects since the selection procedure is data-dependent. Before comparing Bayesian variable selection procedures, we first classify the current Bayesian variable selection procedures into two classes: those with selection criteria defined on the space of candidate models, and those with selection criteria not explicitly formulated on the model space. For selection methods which do not operate on the model space, it is not obvious or well-established how to assess Bayesian selection consistency. By comparing their selection criteria, we establish connections between these classes of selection methods to facilitate discussion of Bayesian variable selection consistency for both classes. Moreover, The former group can be further divided into two sub-classes depending on their use of either the Bayes Factor (BF) or estimates of marginal inclusion probabilities. In the context of linear regression, we first consider the finite sample properties of Bayesian variable selection procedures, focusing on their associated selection uncertainties and their respective empirical frequencies of correct selection, across a broad range of data generating processes. Then we consider Bayesian inference after Bayesian variable selection. Since this type of study is completely new in the Bayesian literature, we must first address many conceptual difficulties in inference after Bayesian variable selection, and more generally Bayesian inference for different types of target parameters that are relevant to the setting of Bayesian variable selection. We give some analytic arguments and simulation-based evidence to illustrate some of the possible selection effects. For population selection problem, we propose a decision-theoretical way to investigate its post-selection inference. In particular, we focus on credible intervals. When the task is to select the best population and construct a credible interval simultaneously, a compound loss function is proposed. We then derive the corresponding Bayes rule, which has both intuitive and theoretical appeal.