FIGURE 3.

Cumulative probability models for the estimation of absolute bacterial abundances. Estimation of class probabilities for each observed value of total microbial load (in CFU), conditional on observed library size, is retrieved from the ordinal logistic regression framework (A). Conditional expectations are then derived as weighted average of microbial load values and respective class probabilities (black line, 95% credible intervals in light blue) (B). The class of highest probability (CHP, the most likely outcome given the observed reads) is also shown (red line, 95% predictive intervals in gray). Posterior predictive check shows the Bayesian model captures the overall structure of the observed data for total microbial load (y_rep: posterior draws, y: observed data) (C). Tail probabilities, herein defined as the probability of observing at least class ck, conditional of observed library size are an alternative for cases in which CHP- and expectation-based predictions are prohibitively uncertain (D). Hierarchical CPM accounts for differences across bacteria and takes advantage of partial pooling to estimate taxon-specific abundances (E). The resulting posterior predictive check indicates no major signs of misfit.