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Abstract
The structure and composition of the microbiota are of critical importance for a variety of areas, including human health, environmental conservation, and bioenergy. To understand the dynamics of the microbiome, interactions between the micobiota and the host or the environment are now frequently studied, but these approaches do not fully take advantage of the phylogenetic structure in the microbiome data and their ad hoc nature make it difficult to accommodate complex experiment designs. Furthermore, the methodology for statistical inference regarding microbiota structure and composition is still quite limited. In order to provide a formal statistical framework, we proposed a variational Bayesian approach to compute the posterior distribution and make inference on the dynamic effect of the host or environmental factors. This method can be seen as an extension of the Factorial Hidden Markov Model with the message passing algorithm over continuous Markov processes. In our examples, variables that associate with the phylogenetic tree represent microbiota structure and composition rather than nucleotide sequences. The computation was performed through a message passing algorithm nested inside the EM algorithm for parameter optimization. We illustrated the application of the proposed method with two actual datasets and used simulation to evaluate its properties. We also proposed further extensions for complex experiment designs and addressed other areas of application.
