Differential Markov random field analysis with an application to detecting differential microbial community networks

: Micro-organisms such as bacteria form complex ecological community networks that can be greatly influenced by diet and other environmental factors. Differential analysis of microbial community structures aims to elucidate systematic changes during an adaptive response to changes in environment. In this paper, we propose a flexible Markov random field model for microbial network structure and introduce a hypothesis testing framework for detecting differences between networks, also known as differential network analysis. Our global test for differential networks is particularly powerful against sparse alternatives. In addition, we develop a multiple testing procedure with false discovery rate control to identify the structure of the differential network. The proposed method is applied to data from a gut microbiome study on U.K. twins to evaluate how age affects the microbial community network.