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.

Keywords: Bayesian methods; Complex data; Genomics; Graphical models; Neuroimaging.

Fig. 1

Posterior probability of inclusion (PPI)

Fig. 2

Multiple myeloma network analyses. Panels (a)-(c). The estimated stage-specific gene co-expression networks. The solid lines indicate positive partial correlations and the dashed lines indicate negative partial correlations. Panel (d). The estimated gene regulatory network from graphical regression integrating the prognostic factors: S${\beta }_2$M and serum albumin. The solid lines with arrowheads indicate positive constant effects; solid lines with flat heads indicate negative constant effects; dashed lines indicate linearly varying effects; dotted lines indicate nonlinearly varying effects; the width of the solid line is proportional to the posterior probability of inclusion

Fig. 3

Nonlinearly (top) and linearly (bottom) varying effects for the multiple myeloma dataset analyzed by the graphical regression model. For each plot, the estimated conditional independence functions (solid) with 95% credible bands (dotted) are shown in the top portion and marginal posterior inclusion probabilities are shown in the bottom portion. Red horizontal line is the 0.5 probability cutoff. Blue (grey) lines and curves indicate (in)significant coefficients