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 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 Assigning G in Zellner s G Prior for Bayesian Variable Selection written by Mengjie Wang and published by . This book was released on 2015 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are numerous frequentist statistics variable selection methods such as Stepwise regression, AIC and BIC etc. In particular, the latter two criteria include a penalty term which discourages overfitting. In terms of the framework of Bayesian variable selection, a popular approach is using Bayes Factor (Kass & Raftery 1995), which also has a natural built-in penalty term (Berger & Pericchi 2001). Zellner's g prior (Zellner 1986) is a common prior for coefficients in the linear regression model due to its computational speed of analytic solutions for posterior. However, the choice of g is a problem which has attracted a lot of attention. (Zellner 1986) pointed out that if g is unknown, a prior can be introduced and g can be integrated out. One of the prior choices is Hyper-g Priors proposed by (Liang et al. 2008). Instead of proposing a prior for g, we will assign a fixed value for g based on controlling the Type I error for the test based on the Bayes factor. Since we are using Bayes factor to do model selection, the test statistic is Bayes factor. Every test comes with a Type I error, so it is reasonable to restrict this error under a critical value, which we will take as benchmark values, such as 0.1 or 0.05. This approach will automatically involve setting a value of g. Based on this idea, a fixed g can be selected, hence avoiding the need to find a prior for g.

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 Frontiers of Statistical Decision Making and Bayesian Analysis written by Ming-Hui Chen and published by Springer Science & Business Media. This book was released on 2010-07-24 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.

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 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 A Bayesian Variable Selection Method with Applications to Spatial Data written by Xiahan Tang and published by . This book was released on 2017 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis first describes the general idea behind Bayes Inference, various sampling methods based on Bayes theorem and many examples. Then a Bayes approach to model selection, called Stochastic Search Variable Selection (SSVS) is discussed. It was originally proposed by George and McCulloch (1993). In a normal regression model where the number of covariates is large, only a small subset tend to be significant most of the times. This Bayes procedure specifies a mixture prior for each of the unknown regression coefficient, the mixture prior was originally proposed by Geweke (1996). This mixture prior will be updated as data becomes available to generate a posterior distribution that assigns higher posterior probabilities to coefficients that are significant in explaining the response. Spatial modeling method is described in this thesis. Prior distribution for all unknown parameters and latent variables are specified. Simulated studies under different models have been implemented to test the efficiency of SSVS. A real dataset taken by choosing a small region from the Cape Floristic Region in South Africa is used to analyze the plants distribution in that region. The original multi-cateogory response is transformed into a presence and absence (binary) response for simpler analysis. First, SSVS is used on this dataset to select the subset of significant covariates. Then a spatial model is fitted using the chosen covariates and, post-estimation, predictive map of posterior probabilities of presence and absence are obtained for the study region. Posterior estimates for the true regression coefficients are also provided along with map for spatial random effects.

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 Using Lasso written by Yuchen Han and published by . This book was released on 2017 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis proposes to combine the Kuo and Mallick approach (1998) and Bayesian Lasso approach (2008) by introducing a Laplace distribution on the conditional prior of the regression parameters given the indicator variables. Gibbs Sampling will be used to sample from the joint posterior distribution. We compare these two new method to existing Bayesian variable selection methods such as Kuo and Mallick, George and McCulloch and Park and Casella and provide an overall qualitative assessment of the efficiency of mixing and separation. We will also use air pollution dataset to test the proposed methodology with the goal of identifying the main factors controlling the pollutant concentration.

Download or read book Bayesian Variable Selection Via a Benchmark written by and published by . This book was released on 2013 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: With increasing appearances of high dimensional data over the past decades, variable selections through likelihood penalization remains a popular yet challenging research area in statistics. Ridge and Lasso, the two of the most popular penalized regression methods, served as the foundation of regularization technique and motivated several extensions to accommodate various circumstances, mostly through frequentist models. These two regularization problems can also be solved by their Bayesian counterparts, via putting proper priors on the regression parameters and then followed by Gibbs sampling. Compared to the frequentist version, the Bayesian framework enables easier interpretation and more straightforward inference on the parameters, based on the posterior distributional results. In general, however, the Bayesian approaches do not provide sparse estimates for the regression coefficients. In this thesis, an innovative Bayesian variable selection method via a benchmark variable in conjunction with a modified BIC is proposed under the framework of linear regression models as the first attempt, to promote both model sparsity and accuracy. The motivation of introducing such a benchmark is discussed, and the statistical properties regarding its role in the model are demonstrated. In short, it serves as a criterion to measure the importance of each variable based on the posterior inference of the corresponding coefficients, and only the most important variables providing the minimal modified BIC value are included. The Bayesian approach via a benchmark is extended to accommodate linear models with covariates exhibiting group structures. An iterative algorithm is implemented to identify both important groups and important variables within the selected groups. What's more, the method is further developed and modified to select variables for generalized linear models, by taking advantage of the normal approximation on the likelihood function. Simulation studies are carried out to assess and compare the performances among the proposed approaches and other state-of-art methods for each of the above three scenarios. The numerical results consistently illustrate our Bayesian variable selection approaches tend to select exactly the true variables or groups, while producing comparable prediction errors as other methods. Besides the numerical work, several real data sets are analyzed by these methods and the corresponding performances are further compared. The variable selection results by our approach are intuitively appealing or consistent with existing literatures in general.

Download or read book Objective Bayesian Variable Selection for Censored Data written by Silvia Perra and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of survival analysis is to explain and predict the survival, usually defined along the time domain. In this work we study it by means of regression models. In statistical data analysis it is common to consider the regression set up in which a given response variable depends on some factors and/or covariates. The model selection problem mainly consists in choosing the covariates which better explain the dependent variable in a precise and hopefully fast manner. This process usually has several steps: the first one is to collect considerations from an expert about the set of covariates, then the statistician derives a prior on model parameters and constructs a tool to solve the model selection problem. We consider the model selection problem in survival analysis when the response variable is the time to event. Under an objective Bayesian approach, some commonly used tools in literature are the Intrinsic Bayes factor (IBF) and the Fractional Bayes factor (FBF). In this thesis we deal with the variable selection problem for censored data.

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.

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 Monte Carlo Simulation and Resampling Methods for Social Science written by Thomas M. Carsey and published by SAGE Publications. This book was released on 2013-08-05 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking the topics of a quantitative methodology course and illustrating them through Monte Carlo simulation, this book examines abstract principles, such as bias, efficiency, and measures of uncertainty in an intuitive, visual way. Instead of thinking in the abstract about what would happen to a particular estimator "in repeated samples," the book uses simulation to actually create those repeated samples and summarize the results. The book includes basic examples appropriate for readers learning the material for the first time, as well as more advanced examples that a researcher might use to evaluate an estimator he or she was using in an actual research project. The book also covers a wide range of topics related to Monte Carlo simulation, such as resampling methods, simulations of substantive theory, simulation of quantities of interest (QI) from model results, and cross-validation. Complete R code from all examples is provided so readers can replicate every analysis presented using R.

Download or read book Flexible Imputation of Missing Data Second Edition written by Stef van Buuren and published by CRC Press. This book was released on 2018-07-17 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Missing data pose challenges to real-life data analysis. Simple ad-hoc fixes, like deletion or mean imputation, only work under highly restrictive conditions, which are often not met in practice. Multiple imputation replaces each missing value by multiple plausible values. The variability between these replacements reflects our ignorance of the true (but missing) value. Each of the completed data set is then analyzed by standard methods, and the results are pooled to obtain unbiased estimates with correct confidence intervals. Multiple imputation is a general approach that also inspires novel solutions to old problems by reformulating the task at hand as a missing-data problem. This is the second edition of a popular book on multiple imputation, focused on explaining the application of methods through detailed worked examples using the MICE package as developed by the author. This new edition incorporates the recent developments in this fast-moving field. This class-tested book avoids mathematical and technical details as much as possible: formulas are accompanied by verbal statements that explain the formula in accessible terms. The book sharpens the reader’s intuition on how to think about missing data, and provides all the tools needed to execute a well-grounded quantitative analysis in the presence of missing data.