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A Bayesian Variable Selection Method With Applications To Spatial Data
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Book Synopsis A Bayesian Variable Selection Method with Applications to Spatial Data by : Xiahan Tang
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.
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 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
Book Synopsis Bayesian Variable Selection and Functional Data Analysis by : Asish Kumar Banik
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.
Book Synopsis A Two-stage Bayesian Variable Selection Method with the Extension of Lasso for Geo-referenced Count Data by : Yuqian Shen
Download or read book A Two-stage Bayesian Variable Selection Method with the Extension of Lasso for Geo-referenced Count Data written by Yuqian Shen and published by . This book was released on 2019 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the complex nature of geo-referenced data, multicollinearity of the risk factors in public health spatial studies is a commonly encountered issue, which leads to low parameter estimation accuracy because it inflates the variance in the regression analysis. To address this issue, we proposed a two-stage variable selection method by extending the least absolute shrinkage and selection operator (Lasso) to the Bayesian spatial setting, investigating the impact of risk factors to health outcomes. Specifically, in stage I, we performed the variable selection using Bayesian Lasso and several other variable selection approaches. Then, in stage II, we performed the model selection with only the selected variables from stage I and compared again the methods. To evaluate the performance of the two-stage variable selection methods, we conducted a simulation study with different distributions for the risk factors, using geo-referenced count data as the outcome and Michigan as the research region. We considered the cases when all candidate risk factors are independently normally distributed, or follow a multivariate normal distribution with different correlation levels. Two other Bayesian variable selection methods, Binary indicator, and the combination of Binary indicator and Lasso are considered and compared as alternative methods. The simulation results indicate that the proposed two-stage Bayesian Lasso variable selection method has the best performance for both independent and dependent cases considered. When compared with the one-stage approach, and the other two alternative methods, the two-stage Bayesian Lasso approach provides the highest estimation accuracy in all scenarios considered.
Book Synopsis Bayesian Variable Selection for High Dimensional Data Analysis by : Yang Aijun
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.
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 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 Incorporating Bayesian Variable Selection Into the Spatial Mixed Effects Models with Process Augmentation by : Jaehui Lim
Download or read book Incorporating Bayesian Variable Selection Into the Spatial Mixed Effects Models with Process Augmentation written by Jaehui Lim and published by . This book was released on 2021 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we introduce a model that we call the Bayesian wavelet neural network (BWNN) for variable selection in the sparsely observed spatio-temporal data setting. Our first attempts were motivated by a process augmentation approach and forward selection, and also included an approach based on the use of credible intervals. Simulation studies indicated several drawbacks of these methods, which motivated many components of the BWNN. The BWNN's first layer models an initial representation of the latent process with a spatial mixed effects model (SME). Then, the BWNN includes a layer defined by the Spike-and-slab (SS) method, which is a well-known Bayesian variable selection method. The SS method represents an initial selection of basis functions and covariates in the BWNN. An additional layer is included to select the final set of features (id est, basis functions and covariates). This layer is another motivating component of BWNN since the SS (by itself) does not use a single set of selected features for modeling. The final layer of the BWNN uses the selected features in a SME model. We demonstrate how to construct the BWNN, and test its prediction accuracy and variable selection ability through various examples. We then fit the BWNN model to GPA data, a motivating dataset of BWNN development, where the data is highly sparse over space and time. Motivated by the BWNN's use of wavelets, we consider BWNN as a new type of wavelet threshold method, which we investigate empirically. Specifically, we make comparisons between BWNN and existing wavelet threshold methods and show empirical results.
Book Synopsis Regression Modelling wih Spatial and Spatial-Temporal Data by : Robert P. Haining
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.
Book Synopsis Bayesian Variable Selection for Non-Gaussian Data Using Global-Local Shrinkage Priors and the Multivaraite Logit-Beta Distribution by : Hongyu Wu
Download or read book Bayesian Variable Selection for Non-Gaussian Data Using Global-Local Shrinkage Priors and the Multivaraite Logit-Beta Distribution written by Hongyu Wu and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variable selection methods have become an important and growing problem in Bayesian analysis. The literature on Bayesian variable selection methods tends to be applied to a single response- type, and more typically, a continuous response-type, where it is assumed that the data is Gaus- sian/symmetric. In this dissertation, we develop a novel global-local shrinkage prior in non- symmetric settings and multiple response-types settings by combining the perspectives of global- local shrinkage and the conjugate multivaraite distribution. In Chapter 2, we focus on the problem of variable selection when the data is possibly non- symmetric continuous-valued. We propose modeling continuous-valued data and the coefficient vector with the multivariate logit-beta (MLB) distribution. To perform variable selection in a Bayesian context we make use of shrinkage global-local priors to enforce sparsity. Specifically, they can be defined as a Gaussian scale mixture of a global shrinkage parameter and a local shrinkage parameter for a regression coefficient. We provide a technical discussion that illustrates that our use of the multivariate logit-beta distribution under a P ́olya-Gamma augmentation scheme has an explicit connection to a well-known global-local shrinkage method (id est, the horseshoe prior) and extends it to possibly non-symmetric data. Moreover, our method can be implemented using an efficient block Gibbs sampler. Evidence of improvements in terms of mean squared error and variable selection as compared to the standard implementation of the horseshoe prior for skewed data settings is provided in simulated and real data examples. In Chapter 3, we direct our attention to the canonical variable selection problem in multiple response-types settings, where the observed dataset consists of multiple response-types (e.g., con- tinuous, count-valued, Bernoulli trials, et cetera). We propose the same global-local shrinkage prior in Chapter 2 but for multiple response-types datasets. The implementation of our Bayesian variable selection method to such data types is straightforward given the fact that the multivariate logit-beta prior is the conjugate prior for several members from the natural exponential family of distributions, which leads to the binomial/beta and negative binomial/beta hierarchical models. Our proposed model not just allows the estimation and selection of independent regression coefficients, but also those of shared regression coefficients across-response-types, which can be used to explicitly model dependence in spatial and time-series settings. An efficient block Gibbs sampler is developed, which is found to be effective in obtaining accurate estimates and variable selection results in simulation studies and an analysis of public health and financial costs from natural disasters in the U.S.
Book Synopsis Spatial Bayesian Variable Selection and FMRI by : Bradley Wright McEvoy
Download or read book Spatial Bayesian Variable Selection and FMRI written by Bradley Wright McEvoy and published by . This book was released on 2009 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Bayesian Variable Selection with Spike-and-slab Priors by : Anjali Agarwal
Download or read book Bayesian Variable Selection with Spike-and-slab Priors written by Anjali Agarwal and published by . This book was released on 2016 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: A major focus of intensive methodological research in recent times has been on knowledge extraction from high-dimensional datasets made available by advances in research technologies. Coupled with the growing popularity of Bayesian methods in statistical analysis, a range of new techniques have evolved that allow innovative model-building and inference in high-dimensional settings – an important one among these being Bayesian variable selection (BVS). The broad goal of this thesis is to explore different BVS methods and demonstrate their application in high-dimensional psychological data analysis. In particular, the focus will be on a class of sparsity-enforcing priors called 'spike-and-slab' priors which are mixture priors on regression coefficients with density functions that are peaked at zero (the 'spike') and also have large probability mass for a wide range of non-zero values (the 'slab'). It is demonstrated that BVS with spike-and-slab priors achieved a reasonable degree of dimensionality-reduction when applied to a psychiatric dataset in a logistic regression setup. BVS performance was also compared to that of LASSO (least absolute shrinkage and selection operator), a popular machine-learning technique, as reported in Ahn et al.(2016). The findings indicate that BVS with a spike-and-slab prior provides a competitive alternative to machine-learning methods, with the additional advantages of ease of interpretation and potential to handle more complex models. In conclusion, this thesis serves to add a new cutting-edge technique to the lab’s tool-shed and helps introduce Bayesian variable-selection to researchers in Cognitive Psychology where it still remains relatively unexplored as a dimensionality-reduction tool.
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 Bayesian Variable Selection in High-dimensional Applications by : Veronika Roc̆ková
Download or read book Bayesian Variable Selection in High-dimensional Applications written by Veronika Roc̆ková and published by . This book was released on 2013 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Book Synopsis Case Studies in Applied Bayesian Data Science by : Kerrie L. Mengersen
Download or read book Case Studies in Applied Bayesian Data Science written by Kerrie L. Mengersen and published by Springer Nature. This book was released on 2020-05-28 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a range of substantive applied problems within Bayesian Statistics along with their Bayesian solutions, this book arises from a research program at CIRM in France in the second semester of 2018, which supported Kerrie Mengersen as a visiting Jean-Morlet Chair and Pierre Pudlo as the local Research Professor. The field of Bayesian statistics has exploded over the past thirty years and is now an established field of research in mathematical statistics and computer science, a key component of data science, and an underpinning methodology in many domains of science, business and social science. Moreover, while remaining naturally entwined, the three arms of Bayesian statistics, namely modelling, computation and inference, have grown into independent research fields. While the research arms of Bayesian statistics continue to grow in many directions, they are harnessed when attention turns to solving substantive applied problems. Each such problem set has its own challenges and hence draws from the suite of research a bespoke solution. The book will be useful for both theoretical and applied statisticians, as well as practitioners, to inspect these solutions in the context of the problems, in order to draw further understanding, awareness and inspiration.
