Efficient Bayesian Additive Regression Models for Microbiome Studies

Abstract

Bayesian multinomial logistic-normal (MLN) models have gained popularity due to their ability to account for the count compositional nature of microbiome data. Recently, we developed a computationally efficient and accurate approach to inferring MLN models with a Marginally Latent Matrix-T Process (MLTP) form: MLN-MLTPs. However, previous research on MLTPs has been restricted to linear models or a single non-linear process. This article addresses this deficiency by introducing a new class of MLN Additive Gaussian Process models (MultiAddGPs) for deconvolution of overlapping linear and non-linear processes. We show that MultiAddGPs are examples of MLN-MLTPs and derive an efficient Collapse-Uncollapse (CU) sampler for this model class. Through simulation studies, we show that MultiAddGPs accurately and efficiently decompose over- lapping effects in microbiota data, which provides a powerful tool for analyzing complex count compositional datasets