Chen, Y. (STAT) – Flexible Bayesian Models for High-Dimensional and Longitudinal Discrete Data in Microbiome Studies

Multivariate dependent discrete data routinely arise in microbiome studies. Analyzing these data presents interesting statistical challenges, such as high dimensionality, excess zeros, large heterogeneity across samples, and temporal dependence in longitudinal studies. Drawing inferences about objects of primary scientific interest—such as temporal trajectories of microbial abundance, microbial interactions, clusters of microbes similarly associated with environmental factors, or networks of conditional dependencies—is more challenging due to these complexities, requiring careful statistical modeling. Motivated by longitudinal microbiome experiments and large-scale fungal community surveys, we propose flexible Bayesian models in which these objects are represented through low-dimensional or sparse structures, regularized by global–local shrinkage priors, and reported with uncertainty propagated through posterior inference. We first develop a Bayesian dynamic latent factor model for multivariate longitudinal count data. A rounded multivariate log-normal kernel links the observed counts to latent Gaussian variables, and treatment-specific temporal trends of microbial abundance are modeled through Bayesian penalized B-splines. To better capture temporal changes in the mean, dependence among microbial features is modeled through a low-dimensional factor structure with a Dirichlet–horseshoe+ shrinkage prior on the loadings. In addition, continuous-time Ornstein–Uhlenbeck processes are used for the latent factors to account for temporal dependence within a subject. We next develop a sparse Bayesian probit regression model for high-dimensional presence–absence data to infer clusters of microbes whose presence has similar associations with environmental covariates. Due to the large number of microbes and excess zeros, we first estimate a high-dimensional regression coefficient matrix using sparsity-inducing priors, and then cluster the microbes based on the coefficient estimates. By using the posterior distribution of the coefficients, we provide point estimates along with uncertainty quantification. Lastly, we develop a Bayesian model that infers a time-varying precision matrix for longitudinal microbiome count data. While a covariance matrix describes marginal dependence, a precision matrix characterizes conditional dependence among microbial features, defining a microbial association network. By allowing this precision structure to evolve over time, we obtain inferences about dynamic microbial networks.

Event Host: Yongqi Chen, Ph.D. Student, Statistical Science

Advisor: Juhee Lee

Zoom: https://ucsc.zoom.us/j/99307567941?pwd=NRnSLblnMKXEgqDRXPdBIFaRS8ctsq.1

Passcode: 301374