Robust Linear Spectral Unmixing using Anomaly Detection

This paper presents a Bayesian algorithm for linear spectral unmixing of hyperspectral images that accounts for anomalies present in the data. The model proposed assumes that the pixel reflectances are linear mixtures of unknown endmembers, corrupted by an additional nonlinear term modelling anomalies and additive Gaussian noise. A Markov random field is used for anomaly detection based on the spatial and spectral structures of the anomalies. This allows outliers to be identified in particular regions and wavelengths of the data cube. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint linear unmixing and anomaly detection algorithm. Simulations conducted with synthetic and real hyperspectral images demonstrate the accuracy of the proposed unmixing and outlier detection strategy for the analysis of hyperspectral images

Partially-Latent Class Models (pLCM) for Case-Control Studies of Childhood Pneumonia Etiology

In population studies on the etiology of disease, one goal is the estimation of the fraction of cases attributable to each of several causes. For example, pneumonia is a clinical diagnosis of lung infection that may be caused by viral, bacterial, fungal, or other pathogens. The study of pneumonia etiology is challenging because directly sampling from the lung to identify the etiologic pathogen is not standard clinical practice in most settings. Instead, measurements from multiple peripheral specimens are made. This paper introduces the statistical methodology designed for estimating the population etiology distribution and the individual etiology probabilities in the Pneumonia Etiology Research for Child Health (PERCH) study of 9; 500 children for 7 sites around the world. We formulate the scientific problem in statistical terms as estimating the mixing weights and latent class indicators under a partially-latent class model (pLCM) that combines heterogeneous measurements with different error rates obtained from a case-control study. We introduce the pLCM as an extension of the latent class model. We also introduce graphical displays of the population data and inferred latent-class frequencies. The methods are tested with simulated data, and then applied to PERCH data. The paper closes with a brief description of extensions of the pLCM to the regression setting and to the case where conditional independence among the measures is relaxed.Comment: 25 pages, 4 figures, 1 supplementary materia

BAYESIAN METHODS FOR CORRELATED PREDICTORS AND CONFOUNDING VARIABLES IN EPIDEMIOLOGY

In epidemiology, it is common to have a set of outcomes, exposures, and confounding variables on different scales (i.e. continuous, count, categorical: nominal/ordinal). Confounding variables are expect to be correlated with exposures and at times exposures may be highly correlated among themselves which present model estimation complications. This is especially prevalent in environmental epidemiology, where studying the joint or simultaneous effect of chemical mixture or air pollution exposures on health for example is of interest. Dimension reduction techniques and shrinkage effect estimation are important tools to overcome these difficulties. Studying the multivariate dependence among mixed scale variables can aid investigators in developing analysis plans but mixed-scale distribution modeling is not a simple task. Specifically, it may be of interest to assess and quantify the degree of correlation among variables and or characterize different exposure-confounding variable profiles. Certain dimension reduction methods, such as, mixture models can do both, as well as, jointly model variables of mixed-scales. Shrinkage methods, on the other hand, do not transform a set of correlated variables but implement a bias-variance trade-off to address effect estimation. The overall goal of this research is to develop a suite of Bayesian methods for clustering via mixed-scale distributional modeling and variable selection. First, motivated by sophisticated Bayesian mixed-scale distribution modeling, we develop a joint model using modularized tensor factorization (MOTEF) as a simplification for ease of implementation and computation. The performance of MOTEF is assessed via a simulation study and applied to data from the National Birth Defects and Prevention Study (NBDPS) for mixed-scale multivariate profiling. Second, we develop a Bayesian semi-parametric model with variable selection for hierarchical interactions (BHIS). Its performance is assessed via simulation studies and applied to the Mount Sinai Children's Environmental Health Study. Lastly, building on Bayesian mixed-scale distribution modeling, we develop a joint mixture model for compositional data with essential zeros. The model is applied to accelerometry-assessed sedentary behavior and physical activity data from the Hispanic Community Health Study / Study of Latinos for describing activity profiles and health risk.Doctor of Philosoph