Make the most of your samples: Bayes factor estimators for high-dimensional models of sequence evolution

Table 3 Model comparison using path sampling (PS) and stepping-stone sampling (SS) for the nuclear SSU rRNA data set

α	K	Q	BDE(PS)	BDE( $\bar{PS}$ )	BDE(SS)	PS-A	PS-M	$\bar{PS} -A$	$\bar{PS} -M$	SS-A	SS-M
6.0	16.000	200	6.76	4.38	4.32	-58.33	-59.82	-58.82	-57.56	-59.35	-56.82
8.0			2.12	1.99	1.89	-58.92	-59.14	-58.69	-59.11	-58.69	-58.91
9.0			2.08	1.89	1.83	-59.37	-59.48	-58.92	-59.36	-59.00	-59.23
10.0			2.00	1.66	1.64	-60.47	-59.96	-59.94	-59.47	-59.97	-59.38
11.0			2.60	2.74	2.69	-58.89	-59.15	-58.86	-59.23	-58.89	-59.12
12.0			1.86	1.93	2.04	-59.54	-58.80	-59.55	-58.53	-59.57	-58.43
13.0			2.47	2.12	2.20	-58.58	-59.10	-58.44	-59.00	-58.46	-58.87

Nuclear SSU rRNA data set. Log Bayes factor estimates for the context-dependent model compared to the site-independent model using regular path sampling (PS; only using the last sample for each path step), path sampling using the mean of a collection of samples from each path step ( $\bar{PS}$ ) and regular stepping-stone sampling (SS). Bidirectional checks, consisting of annealing (-A) and melting (-M) integrations, were performed for each log Bayes factor calculation, yielding a bidirectional error (BDE) for each estimator. α values indicate the shape of the sigmoid function used to construct a path between the two models. K indicates the number of path steps (or ratios for SS) used, while Q indicates the number of iterations to be performed per path step (or ratio for SS).