Bayesian Variable Selection With Applications To Neuroimaging Data
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Bayesian Variable Selection with Applications to Neuroimaging Data
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.
Handbook of Bayesian Variable Selection
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
Bayesian Estimation and Inference in Computational Anatomy and Neuroimaging: Methods & Applications
Computational Anatomy (CA) is an emerging discipline aiming to understand anatomy by utilizing a comprehensive set of mathematical tools. CA focuses on providing precise statistical encodings of anatomy with direct application to a broad range of biological and medical settings. During the past two decades, there has been an ever-increasing pace in the development of neuroimaging techniques, delivering in vivo information on the anatomy and physiological signals of different human organs through a variety of imaging modalities such as MRI, x-ray, CT, and PET. These multi-modality medical images provide valuable data for accurate interpretation and estimation of various biological parameters such as anatomical labels, disease types, cognitive states, functional connectivity between distinct anatomical regions, as well as activation responses to specific stimuli. In the era of big neuroimaging data, Bayes’ theorem provides a powerful tool to deliver statistical conclusions by combining the current information and prior experience. When sufficiently good data is available, Bayes’ theorem can utilize it fully and provide statistical inferences/estimations with the least error rate. Bayes’ theorem arose roughly three hundred years ago and has seen extensive application in many fields of science and technology, including recent neuroimaging, ever since. The last fifteen years have seen a great deal of success in the application of Bayes’ theorem to the field of CA and neuroimaging. That said, given that the power and success of Bayes’ rule largely depends on the validity of its probabilistic inputs, it is still a challenge to perform Bayesian estimation and inference on the typically noisy neuroimaging data of the real world. We assembled contributions focusing on recent developments in CA and neuroimaging through Bayesian estimation and inference, in terms of both methodologies and applications. It is anticipated that the articles in this Research Topic will provide a greater insight into the field of Bayesian imaging analysis.