Algorithm 2 (Gibbs Sampling Algorithm for the Metagenomic Model).

Require: references species $M$ , metagenomic reads $R$ , hyperparameter $\overrightarrow{\alpha }$ Global data: count statistics $\overrightarrow{n}$ , read-composition distributions $\mathsf{\Phi }$ , memory for full conditionals $p\{z_i|{\overrightarrow{z}}_{\neg i},R;\overrightarrow{\alpha },\mathsf{\Phi }\}$ Ensure: mixture parameters $\overrightarrow{\theta }$ //initialization: obtain read-composition distributions $\mathsf{\Phi }$ according to alignment results zero all count statistics $\overrightarrow{n}$ for $i=1$ to $N$ do sample the species index $z_i=m\sim Mult(M)$ increment sampled species count $n_m=n_m+1$ end for //Gibbs sampling while not finished do for $i=1$ to $N$ do decrement target species count $n_m=n_m-1$ sample a new species index $z_i=\tilde{m}\sim p\{z_i|{\overrightarrow{z}}_{\neg i},R;\overrightarrow{\alpha },\mathsf{\Phi }\}$ increment sampled species’ count $n_{\tilde{m}}=n_{\tilde{m}}+1$ end for if converged and a given number of samples generated then return mixture parameter $\overrightarrow{\theta }$ according to the equation end if end while