Bayesian graphical models for modern biological applications

Abstract

Graphical models are powerful tools that are regularly used to investigate complex dependence structures in high-throughput biomedical datasets. They allow for holistic, systems-level view of the various biological processes, for intuitive and rigorous understanding and interpretations. In the context of large networks, Bayesian approaches are particularly suitable because it encourages sparsity of the graphs, incorporate prior information, and most importantly account for uncertainty in the graph structure. These features are particularly important in applications with limited sample size, including genomics and imaging studies. In this paper, we review several recently developed techniques for the analysis of large networks under non-standard settings, including but not limited to, multiple graphs for data observed from multiple related subgroups, graphical regression approaches used for the analysis of networks that change with covariates, and other complex sampling and structural settings. We also illustrate the practical utility of some of these methods using examples in cancer genomics and neuroimaging.

Bayesian Learning of Graph Substructures

“…See Fienberg (2012) and Barabási (2016) for an overview. Such developments contrast with the literature on graphical models (Friedman et al, 2007;Armstrong et al, 2009;Zhou et al, 2011;Maathuis et al, 2019;Ni et al, 2022) that aims to infer a graph from multivariate data. In this context, focus of inference is usually to determine the presence of an edge between two nodes whereas modelling of large-scale graph structures is often neglected (Bornn and Caron, 2011).…”

Discussion to: Bayesian graphical models for modern biological applications by Y. Ni, V. Baladandayuthapani, M. Vannucci and F.C. Stingo

“…The authors of Dobra et al (2004) hoped that, after the graphs have been determined, the methodological issues they had to solve were over. They (perhaps naively) thought that the resulting graphs will be interpreted in the same manner as Gaussian graphical models are usually interpreted: vertices representing variables (genes in this application) that belong to different connected components will indicate independence of these genes, and vertices not linked by an edge will indicate conditional independence of the corresponding genes-see Section 2.1 of Ni et al (2021). Independence relationships are certainly easier to explain to biologists: genes that cannot be linked through a path of edges in a biological network are unlikely to be activated through the same pathway.…”

“…What we attempt to point out with this discussion is that the interpretability of graphical models (the main motivation for their use in the analysis of complex biological networks) becomes problematic even for single Gaussian graphical models due to the sheer size of the network involved. The paper Ni et al (2021) does a fabulous job in terms of explaining the types of graphical models under consideration, the specification of priors for corresponding Bayesian frameworks for fitting these models, technical details of the MCMC sampling algorithms, and so on. Nevertheless, we feel that methods for interpreting graphs for the significantly more involved types of data covered in Ni et al (2021) are very important especially for communicating the results of statistical analyses to applied researchers.…”

“…The paper Ni et al (2021) does a fabulous job in terms of explaining the types of graphical models under consideration, the specification of priors for corresponding Bayesian frameworks for fitting these models, technical details of the MCMC sampling algorithms, and so on. Nevertheless, we feel that methods for interpreting graphs for the significantly more involved types of data covered in Ni et al (2021) are very important especially for communicating the results of statistical analyses to applied researchers. Such methods do not seem to receive sufficient attention in Ni et al (2021), especially since they are not well developed in the existent literature.…”

“…Nevertheless, we feel that methods for interpreting graphs for the significantly more involved types of data covered in Ni et al (2021) are very important especially for communicating the results of statistical analyses to applied researchers. Such methods do not seem to receive sufficient attention in Ni et al (2021), especially since they are not well developed in the existent literature.…”