Christine B. Peterson

Kevin McCoy, Zachary Wooten, Christine B. Peterson

Measurement error is prevalent across all domains of scientific research where only imprecise observations, rather than the true underlying values, can be obtained. For example, estimates of human microbiome diversity are based on small samples from a much larger, generally unobserved system and reflect both sampling error and technical variation. In high-noise settings like these, it becomes difficult to make accurate predictions and to summarize uncertainty. Methods have previously been proposed to accommodate measurement error in classic predictive models, such as linear regression. However, relatively little work has been done to address measurement error in more complex and flexible models. Bayesian additive regression trees (BART), a Bayesian nonparametric model that sums the output of many decision trees, offers robust predictions with built-in uncertainty quantification. In this work, we propose measurement error BART (meBART), a novel extension to the BART model that directly incorporates measurement error in the independent variable(s). Through simulation studies, we show that in the presence of measurement error, our model enables more accurate parameter estimation, more robust uncertainty quantification, and superior predictive performance. We illustrate the utility of our proposed approach through two biomedical applications where the predictors of interest are subject to measurement error.

Nathan Osborne, Christine B. Peterson, Marina Vannucci

Network estimation and variable selection have been extensively studied in the statistical literature, but only recently have those two challenges been addressed simultaneously. In this paper, we seek to develop a novel method to simultaneously estimate network interactions and associations to relevant covariates for count data, and specifically for compositional data, which have a fixed sum constraint. We use a hierarchical Bayesian model with latent layers and employ spike-and-slab priors for both edge and covariate selection. For posterior inference, we develop a novel variational inference scheme with an expectation maximization step, to enable efficient estimation. Through simulation studies, we demonstrate that the proposed model outperforms existing methods in its accuracy of network recovery. We show the practical utility of our model via an application to microbiome data. The human microbiome has been shown to contribute to many of the functions of the human body, and also to be linked with a number of diseases. In our application, we seek to better understand the interaction between microbes and relevant covariates, as well as the interaction of microbes with each other. We provide a Python implementation of our algorithm, called SINC (Simultaneous Inference for Networks and Covariates), available online.

Genevera I. Allen, Christine Peterson, Marina Vannucci et al.

High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension reduction techniques in the context of supervised data analysis. We introduce a framework for Regularized PLS by solving a relaxation of the SIMPLS optimization problem with penalties on the PLS loadings vectors. Our approach enjoys many advantages including flexibility, general penalties, easy interpretation of results, and fast computation in high-dimensional settings. We also outline extensions of our methods leading to novel methods for Non-negative PLS and Generalized PLS, an adaption of PLS for structured data. We demonstrate the utility of our methods through simulations and a case study on proton Nuclear Magnetic Resonance (NMR) spectroscopy data.