Download or read book Application of Spatial Bayesian Hierarchical Model with Variable Selection to FMRI Data written by and published by . This book was released on 2015 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Application of Spatial Bayesian Hierarchical Models to FMRI Data written by Kuo-Jung Lee and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian modelling has attracted great interest in cognitive science and offered a flexible and interpretable way to study cognitive processes using functional magnetic resonance imaging data. In this chapter, a spatial Bayesian hierarchical model is applied to an event-related fMRI study of cognitive control using the Simon test. We consider a sparse spatial generalized linear mixed-effects model to capture the spatial dependence among activated voxels and temporal parameters and to benefit computationally by reducing dimensionality. We demonstrate that the proposed model has the capability of identification of the brain areas related to cognitive tasks. Moreover, the reduction in the false positive rate is observed in the simulation study, and the relevant brain regions involved in processing cognitive control are clearly detected in a real-life fMRI example.

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:

Download or read book Bayesian Variable Selection with Applications to Neuroimaging Data written by Shariq Mohammed and published by . This book was released on 2018 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we discuss Bayesian modeling approaches for identifying brain regions that respond to certain stimulus and use them to classify subjects. We specifically deal with multi-subject electroencephalography (EEG) data where the responses are binary, and the covariates are matrices, with measurements taken for each subject at different locations across multiple time points. EEG data has a complex structure with both spatial and temporal attributes to it. We use a divide and conquer strategy to build multiple local models, that is, one model at each time point separately both, to avoid the curse of dimensionality and to achieve computational feasibility. Within each local model, we use Bayesian variable selection approaches to identify the locations which respond to a stimulus. We use continuous spike and slab prior, which has inherent variable selection properties. We initially demonstrate the local Bayesian modeling approach which is computationally inexpensive, where the estimation for each local modeling could be conducted in parallel. We use MCMC sampling procedures for parameter estimation. We also discuss a two-stage variable selection approach based on thresholding using the complexity parameter built within the model. A prediction strategy is built utilizing the temporal structure between local models. The spatial correlation is incorporated within the local Bayesian modeling to improve the inference. The temporal characteristic of the data is incorporated through the prior structure by learning from the local models estimated at previous time points. Variable selection is done via clustering of the locations based on their activation time. We then use a weighted prediction strategy to pool information from the local spatial models to make a final prediction. Since the EEG data has both spatial and temporal correlations acting simultaneously, we enrich our local Bayesian modeling by incorporating both correlations through a Kronecker product of the spatial and temporal correlation structures. We develop a highly scalable estimation approach to deal with the ultra-huge number of parameters in the model. We demonstrate the efficiency of estimation using the scalable algorithm by performing simulation studies. We also study the performance of these models through a case study on multi-subject EEG data.

Download or read book Computational Issues in Using Bayesian Hierarchical Methods for the Spatial Modeling of FMRI Data written by Kuo-Jung Lee and published by . This book was released on 2010 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Regression Modelling wih Spatial and Spatial Temporal Data written by Robert P. Haining and published by CRC Press. This book was released on 2020-01-27 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling Spatial and Spatial-Temporal Data: A Bayesian Approach is aimed at statisticians and quantitative social, economic and public health students and researchers who work with spatial and spatial-temporal data. It assumes a grounding in statistical theory up to the standard linear regression model. The book compares both hierarchical and spatial econometric modelling, providing both a reference and a teaching text with exercises in each chapter. The book provides a fully Bayesian, self-contained, treatment of the underlying statistical theory, with chapters dedicated to substantive applications. The book includes WinBUGS code and R code and all datasets are available online. Part I covers fundamental issues arising when modelling spatial and spatial-temporal data. Part II focuses on modelling cross-sectional spatial data and begins by describing exploratory methods that help guide the modelling process. There are then two theoretical chapters on Bayesian models and a chapter of applications. Two chapters follow on spatial econometric modelling, one describing different models, the other substantive applications. Part III discusses modelling spatial-temporal data, first introducing models for time series data. Exploratory methods for detecting different types of space-time interaction are presented followed by two chapters on the theory of space-time separable (without space-time interaction) and inseparable (with space-time interaction) models. An applications chapter includes: the evaluation of a policy intervention; analysing the temporal dynamics of crime hotspots; chronic disease surveillance; and testing for evidence of spatial spillovers in the spread of an infectious disease. A final chapter suggests some future directions and challenges.

Download or read book Modelling Spatial and Spatial Temporal Data A Bayesian Approach written by Robert P. Haining and published by CRC Press. This book was released on 2020-01-27 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling Spatial and Spatial-Temporal Data: A Bayesian Approach is aimed at statisticians and quantitative social, economic and public health students and researchers who work with spatial and spatial-temporal data. It assumes a grounding in statistical theory up to the standard linear regression model. The book compares both hierarchical and spatial econometric modelling, providing both a reference and a teaching text with exercises in each chapter. The book provides a fully Bayesian, self-contained, treatment of the underlying statistical theory, with chapters dedicated to substantive applications. The book includes WinBUGS code and R code and all datasets are available online. Part I covers fundamental issues arising when modelling spatial and spatial-temporal data. Part II focuses on modelling cross-sectional spatial data and begins by describing exploratory methods that help guide the modelling process. There are then two theoretical chapters on Bayesian models and a chapter of applications. Two chapters follow on spatial econometric modelling, one describing different models, the other substantive applications. Part III discusses modelling spatial-temporal data, first introducing models for time series data. Exploratory methods for detecting different types of space-time interaction are presented followed by two chapters on the theory of space-time separable (without space-time interaction) and inseparable (with space-time interaction) models. An applications chapter includes: the evaluation of a policy intervention; analysing the temporal dynamics of crime hotspots; chronic disease surveillance; and testing for evidence of spatial spillovers in the spread of an infectious disease. A final chapter suggests some future directions and challenges.

Download or read book A Bayesian Multi Stage Spatio Temporally Dependent Model for Spatial Clustering and Variable Selection written by Shaopei Ma and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In spatio-temporal epidemiological analysis, it is of critical importance to identify the significant covariates and estimate the associated time-varying effects on the health outcome. Due to the heterogeneity of spatio-temporal data, the subsets of important covariates may vary across space and the temporal trends of covariate effects could be locally different. However, many spatial models neglected the potential local variation patterns, leading to inappropriate inference. Thus, this paper proposes a flexible Bayesian hierarchical model to simultaneously identify spatial clusters of regression coefficients with common temporal trends, select significant covariates for each spatial group by introducing binary entry parameters and estimate spatio-temporally varying disease risks. A multi-stage strategy is employed to reduce the confounding bias caused by spatially structured random components. A simulation study demonstrates the outperformance of the proposed method, compared with several alternatives based on different assessment criteria. The methodology is motivated by two important case studies. The first concerns the low birth weight incidence data in 159 counties of Georgia, USA, for the years 2007-2018 and investigates the time-varying effects of potential contributing covariates in different cluster regions. The second concerns the circulatory disease risks across 323 local authorities in England over 10 years and explores the underlying spatial clusters and associated important risk factors.

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 Application of Bayesian Spatial Models in Multi source Forest Inventory written by Andrew O. Finley and published by . This book was released on 2006 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bayesian Biostatistics written by Emmanuel Lesaffre and published by John Wiley & Sons. This book was released on 2012-08-13 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: The growth of biostatistics has been phenomenal in recent years and has been marked by considerable technical innovation in both methodology and computational practicality. One area that has experienced significant growth is Bayesian methods. The growing use of Bayesian methodology has taken place partly due to an increasing number of practitioners valuing the Bayesian paradigm as matching that of scientific discovery. In addition, computational advances have allowed for more complex models to be fitted routinely to realistic data sets. Through examples, exercises and a combination of introductory and more advanced chapters, this book provides an invaluable understanding of the complex world of biomedical statistics illustrated via a diverse range of applications taken from epidemiology, exploratory clinical studies, health promotion studies, image analysis and clinical trials. Key Features: Provides an authoritative account of Bayesian methodology, from its most basic elements to its practical implementation, with an emphasis on healthcare techniques. Contains introductory explanations of Bayesian principles common to all areas of application. Presents clear and concise examples in biostatistics applications such as clinical trials, longitudinal studies, bioassay, survival, image analysis and bioinformatics. Illustrated throughout with examples using software including WinBUGS, OpenBUGS, SAS and various dedicated R programs. Highlights the differences between the Bayesian and classical approaches. Supported by an accompanying website hosting free software and case study guides. Bayesian Biostatistics introduces the reader smoothly into the Bayesian statistical methods with chapters that gradually increase in level of complexity. Master students in biostatistics, applied statisticians and all researchers with a good background in classical statistics who have interest in Bayesian methods will find this book useful.

Download or read book Scalable Bayesian spatial analysis with Gaussian Markov random fields written by Per Sidén and published by Linköping University Electronic Press. This book was released on 2020-08-17 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accurate statistical analysis of spatial data is important in many applications. Failing to properly account for spatial autocorrelation may often lead to false conclusions. At the same time, the ever-increasing sizes of spatial datasets pose a great computational challenge, as many standard methods for spatial analysis are limited to a few thousand data points. In this thesis, we explore how Gaussian Markov random fields (GMRFs) can be used for scalable analysis of spatial data. GMRFs are closely connected to the commonly used Gaussian processes, but have sparsity properties that make them computationally cheap both in time and memory. The Bayesian framework enables a GMRF to be used as a spatial prior, comprising the assumption of smooth variation over space, and gives a principled way to estimate the parameters and propagate uncertainty. We develop new algorithms that enable applying GMRF priors in 3D to the brain activity inherent in functional magnetic resonance imaging (fMRI) data, with millions of observations. We show that our methods are both faster and more accurate than previous work. A method for approximating selected elements of the inverse precision matrix (i.e. the covariance matrix) is also proposed, which is important for evaluating the posterior uncertainty. In addition, we establish a link between GMRFs and deep convolutional neural networks, which have been successfully used in countless machine learning tasks for images, resulting in a deep GMRF model. Finally, we show how GMRFs can be used in real-time robotic search and rescue operations, for modeling the spatial distribution of injured persons. Tillförlitlig statistisk analys av spatiala data är viktigt inom många tillämpningar. Om inte korrekt hänsyn tas till spatial autokorrelation kan det ofta leda till felaktiga slutsatser. Samtidigt ökar ständigt storleken på de spatiala datamaterialen vilket utgör en stor beräkningsmässig utmaning, eftersom många standardmetoder för spatial analys är begränsade till några tusental datapunkter. I denna avhandling utforskar vi hur Gaussiska Markov-fält (eng: Gaussian Markov random fields, GMRF) kan användas för mer skalbara analyser av spatiala data. GMRF-modeller är nära besläktade med de ofta använda Gaussiska processerna, men har gleshetsegenskaper som gör dem beräkningsmässigt effektiva både vad gäller tids- och minnesåtgång. Det Bayesianska synsättet gör det möjligt att använda GMRF som en spatial prior som innefattar antagandet om långsam spatial variation och ger ett principiellt tillvägagångssätt för att skatta parametrar och propagera osäkerhet. Vi utvecklar nya algoritmer som gör det möjligt att använda GMRF-priors i 3D för den hjärnaktivitet som indirekt kan observeras i hjärnbilder framtagna med tekniken fMRI, som innehåller milliontals datapunkter. Vi visar att våra metoder är både snabbare och mer korrekta än tidigare forskning. En metod för att approximera utvalda element i den inversa precisionsmatrisen (dvs. kovariansmatrisen) framförs också, vilket är viktigt för att kunna evaluera osäkerheten i posteriorn. Vidare gör vi en koppling mellan GMRF och djupa neurala faltningsnätverk, som har använts framgångsrikt för mängder av bildrelaterade problem inom maskininlärning, vilket mynnar ut i en djup GMRF-modell. Slutligen visar vi hur GMRF kan användas i realtid av autonoma drönare för räddningsinsatser i katastrofområden för att modellera den spatiala fördelningen av skadade personer.

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 Assessing Brain Activity Through Spatial Bayesian Variable Selection written by and published by . This book was released on 2003 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical parametric mapping (SPM), relying on the general linear model and classical hypothesis testing, is a benchmark tool for assessing human brain activity using data from fMRI experiments. Friston et al. (2002a) discuss some limitations of this frequentist approach and point out promising Bayesian perspectives. In particular, a Bayesian formulation allows explicit modeling and estimation of activation probabilities. In this paper, we directly address this issue and develop a new regression based approach using spatial Bayesian variable selection. Our method has several advantages. First, spatial correlation is directly modeled for activation probabilities and indirectly for activation amplitudes. As a consequence, there is no need for spatial adjustment in a post-processing step. Second, anatomical prior information, such as the distribution of grey matter or expert knowledge, can be included as part of the model. Third, the method has superior edge-preservation properties as well as being fast to compute. When applied to data from a simple visual experiment, the results demonstrate improved sensitivity for detecting activated cortical areas and for better preserving details of activated structures.

Download or read book Statistical Parametric Mapping The Analysis of Functional Brain Images written by William D. Penny and published by Elsevier. This book was released on 2011-04-28 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an age where the amount of data collected from brain imaging is increasing constantly, it is of critical importance to analyse those data within an accepted framework to ensure proper integration and comparison of the information collected. This book describes the ideas and procedures that underlie the analysis of signals produced by the brain. The aim is to understand how the brain works, in terms of its functional architecture and dynamics. This book provides the background and methodology for the analysis of all types of brain imaging data, from functional magnetic resonance imaging to magnetoencephalography. Critically, Statistical Parametric Mapping provides a widely accepted conceptual framework which allows treatment of all these different modalities. This rests on an understanding of the brain's functional anatomy and the way that measured signals are caused experimentally. The book takes the reader from the basic concepts underlying the analysis of neuroimaging data to cutting edge approaches that would be difficult to find in any other source. Critically, the material is presented in an incremental way so that the reader can understand the precedents for each new development. This book will be particularly useful to neuroscientists engaged in any form of brain mapping; who have to contend with the real-world problems of data analysis and understanding the techniques they are using. It is primarily a scientific treatment and a didactic introduction to the analysis of brain imaging data. It can be used as both a textbook for students and scientists starting to use the techniques, as well as a reference for practicing neuroscientists. The book also serves as a companion to the software packages that have been developed for brain imaging data analysis. An essential reference and companion for users of the SPM software Provides a complete description of the concepts and procedures entailed by the analysis of brain images Offers full didactic treatment of the basic mathematics behind the analysis of brain imaging data Stands as a compendium of all the advances in neuroimaging data analysis over the past decade Adopts an easy to understand and incremental approach that takes the reader from basic statistics to state of the art approaches such as Variational Bayes Structured treatment of data analysis issues that links different modalities and models Includes a series of appendices and tutorial-style chapters that makes even the most sophisticated approaches accessible

Download or read book Hierarchical Bayesian Regression with Application in Spatial Modeling and Outlier Detection written by Ghadeer Jasim Mahdi and published by . This book was released on 2018 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation makes two important contributions to the development of Bayesian hierarchical models. The first contribution is focused on spatial modeling. Spatial data observed on a group of areal units is common in scientific applications. The usual hierarchical approach for modeling this kind of dataset is to introduce a spatial random effect with an autoregressive prior. However, the usual Markov chain Monte Carlo scheme for this hierarchical framework requires the spatial effects to be sampled from their full conditional posteriors one-by-one resulting in poor mixing. More importantly, it makes the model computationally inefficient for datasets with large number of units. In this dissertation, we propose a Bayesian approach that uses the spectral structure of the adjacency to construct a low-rank expansion for modeling spatial dependence. We develop a computationally efficient estimation scheme that adaptively selects the functions most important to capture the variation in response. Through simulation studies, we validate the computational efficiency as well as predictive accuracy of our method. Finally, we present an important real-world application of the proposed methodology on a massive plant abundance dataset from Cape Floristic Region in South Africa. The second contribution of this dissertation is a heavy tailed hierarchical regression to detect outliers. We aim to build a linear model that can allow for small as well as large magnitudes of residuals through observation-specific error distribution. t-distribution is specifically suited for that purpose as we can parametrically control its degrees of freedom (df) to tune the heaviness of its tail - large df values represent observations in normal range and small ones represents potential outliers with high error magnitudes. In a hierarchical structure, we can write t-distribution as a scale mixture of a Gaussian distribution so that the standard MCMC algorithm for Gaussian setting can still be used. Post-MCMC, the posterior mean of degrees of freedom for any observation acts as a measure of outlyingness of that observation. We implemented this method on a real dataset consisting of biometric records.

Download or read book Conjugate Hierarchical Models for Spatial Data written by John Jacob McBride and published by . This book was released on 2006 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of generalized linear models provides a unifying class of statistical distributions that can be used to model both discrete and continuous events. In this dissertation we present a new conjugate hierarchical Bayesian generalized linear model that can be used to model counts of occurrences in the presence of spatial correlation. We assume that the counts are taken from geographic regions or areal units (zip codes, counties, etc.) and that the conditional distributions of these counts for each area are distributed as Poisson having unknown rates or relative risks. We incorporate the spatial association of the counts through a neighborhood structure which is based on the arrangement of the areal units. Having defined the neighborhood structure we then model this spatial association with a conditionally autoregressive (CAR) model as developed by Besag (1974). Once the spatial model has been created we adapt a subset selection procedure created by Bratcher and Bhalla (1974) to select the areal unit(s) having the highest relative risks.