Figure 7

As more alignment samples are taken, the DAG-based estimate of the log posterior probability for each alignment converges towards the true value. The DAG-based probabilities already yield a good estimate when the number of alignments, N, is just 100. Shown on the top row are the reconstructed probabilities derived using pair marginals, and on the bottom using the mean field approximation, with the line y=x overlaid in red. Since each sampled alignment is generally observed only once, the posterior probability estimated directly from alignment frequency would be 1/N in each case above. The DAG methodology therefore offers a clear advantage for the purposes of computing posterior alignment probabilities. The mean-field approximation results in a lower mean-squared error (MSE), due to the higher effective sample size (see Figure 6).