Bayesian Statistics Seminar
North Carolina State University
Ixavier Higgins, Emory University
Arkaprava Roy, North Carolina State University
Bo Ning, North Carolina State University
Titles and Abstracts:
Title: Analysis of the Human Brain Connectome
Graph theory has become an increasingly important tool for understanding the brain’s functional organization in health and disease. Despite the rapid development of methods for estimating and comparing functional brain networks across populations, various challenges still persist. For example, it is known that anatomical pathways constrain functional activity in the brain but very few approaches flexibly incorporate this auxiliary information into the estimation of functional connectivity. Furthermore, there are limited statistical methodologies for identifying population level differences in network composition. In this dissertation, we develop methods to address these limitations. First, we propose a method to identify brain regions incident to a large number of edges that are differentially weighted across populations. We achieve this by generating an appropriate set of null networks which are matched on the first and second moments of the observed network using the HQS algorithm. This formulation permits separation of the network’s true topology from that induced by the correlation measure. Next, we propose a method which incorporates structural knowledge into the estimation of functional brain networks. We develop a hierarchical Bayesian Gaussian graphical model which represents the brain functional networks via sparse precision matrices whose degree of edge-specific shrinkage is a random variable informed by anatomical structure and an independent baseline component. The proposed approach flexibly identifies functional connections supported by structural connectivity. This enables robust brain network estimation even in the presence of mis-specified anatomical knowledge while accommodating heterogeneity in the structure-function relationship. Through extensive numerical simulations and applications to imaging data, we show that our proposed methods outperform competitors.
Presenter: Arkaprava Roy
Title: High dimensional single index modeling with application to Brain Atrophy
We study the effects of gender, APOE genes, age, genetic variation and Alzheimer's disease on the atrophy of the brain regions. In the real data analysis section, we add a subject-specific random effect to capture subject inhomogeneity. A nonparametric single index Bayesian model is proposed to study the data with B-spline series prior on the unknown functions and Dirichlet process scale mixture of zero mean normal prior on the distributions of the random effects. A new Bayesian estimation procedure for high dimensional single index model is introduced in this paper. Performance of the proposed Bayesian method is compared with the corresponding least square estimator in the linear model with LASSO and SCAD penalization on the high dimensional covariates. The proposed Bayesian method is applied on a dataset of 748 individuals with 620,901 SNPs and 6 other covariates for each individual.
Presenter: Bo Ning
Title: Nonparametric Prediction and the Exoplanet Mass-Radius Relationship
Statistical estimation of the joint distribution of exoplanet masses and radii plays a fundamental role in understanding the physical and chemical composition of exoplanets. The majority of recent works in this active area of astronomy are based on an assumed parametric power-law regression model for masses as a function of radii. However, there are some arbitrary choices made in the parametric model, including how to choose a proper distribution to describe the intrinsic scatter of masses; how to choose the functional radius dependence of that distribution's variance; and even whether to assume a power-law function or not. In this paper, we present a nonparametric model to estimate the underlying joint distribution of masses and radii for exoplanets. We found that a power-law is a valid assumption for the planets with radius less than 4 R Earth. We also found the variance of the conditional distribution is not a constant. Furthermore, we applied our model to a larger dataset which consists of all the Kepler observations in the NASA Exoplanet Archive. Finally, we created a tool for astronomers to predict planet mass given its radius.
Thursday, March 15 2018,