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Browsing Statistics Publications by Subject "Bayesian hierarchical model"
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Item A Hierarchical Bayesian Model for the Identification of PET Markers Associated to the Prediction of Surgical Outcome after Anterior Temporal Lobe Resection(Frontiers Media S.A., 2017) Chiang, Sharon; Guindani, Michele; Yeh, Hsiang J.; Dewar, Sandra; Haneef, Zulfi; Stern, John M.; Vannucci, MarinaWe develop an integrative Bayesian predictive modeling framework that identifies individual pathological brain states based on the selection of fluoro-deoxyglucose positron emission tomography (PET) imaging biomarkers and evaluates the association of those states with a clinical outcome. We consider data from a study on temporal lobe epilepsy (TLE) patients who subsequently underwent anterior temporal lobe resection. Our modeling framework looks at the observed profiles of regional glucose metabolism in PET as the phenotypic manifestation of a latent individual pathologic state, which is assumed to vary across the population. The modeling strategy we adopt allows the identification of patient subgroups characterized by latent pathologies differentially associated to the clinical outcome of interest. It also identifies imaging biomarkers characterizing the pathological states of the subjects. In the data application, we identify a subgroup of TLE patients at high risk for post-surgical seizure recurrence after anterior temporal lobe resection, together with a set of discriminatory brain regions that can be used to distinguish the latent subgroups. We show that the proposed method achieves high cross-validated accuracy in predicting post-surgical seizure recurrence.Item Smoothing and Mean–Covariance Estimation of Functional Data with a Bayesian Hierarchical Model(Project Euclid, 2016) Yang, Jingjing; Zhu, Hongxiao; Choi, Taeryon; Cox, Dennis D.Functional data, with basic observational units being functions (e.g., curves, surfaces) varying over a continuum, are frequently encountered in various applications. While many statistical tools have been developed for functional data analysis, the issue of smoothing all functional observations simultaneously is less studied. Existing methods often focus on smoothing each individual function separately, at the risk of removing important systematic patterns common across functions. We propose a nonparametric Bayesian approach to smooth all functional observations simultaneously and nonparametrically. In the proposed approach, we assume that the functional observations are independent Gaussian processes subject to a common level of measurement errors, enabling the borrowing of strength across all observations. Unlike most Gaussian process regression models that rely on pre-specified structures for the covariance kernel, we adopt a hierarchical framework by assuming a Gaussian process prior for the mean function and an Inverse-Wishart process prior for the covariance function. These prior assumptions induce an automatic mean–covariance estimation in the posterior inference in addition to the simultaneous smoothing of all observations. Such a hierarchical framework is flexible enough to incorporate functional data with different characteristics, including data measured on either common or uncommon grids, and data with either stationary or nonstationary covariance structures. Simulations and real data analysis demonstrate that, in comparison with alternative methods, the proposed Bayesian approach achieves better smoothing accuracy and comparable mean–covariance estimation results. Furthermore, it can successfully retain the systematic patterns in the functional observations that are usually neglected by the existing functional data analyses based on individual-curve smoothing.