Fig. 4

Real data: Marginal posterior probabilities of inclusion (PPI) for each coefficient β jp, in Eq. (2), describing the association between each taxa and each covariate. Each PPI is obtained by averaging the number of times that each taxa/covariate association is included across the MCMC iterations, after burn-in. Here, the median model, corresponding to a threshold of 0.5 on the PPIs, selects 92 associations. Among those, 26 have a marginal PPI greater than 0.98, which corresponds to a Bayesian FDR of 0.1. These 26 associations are indicated as red dots