Table 3.
Marginal likelihoods, Bayes factors and hypothesis testing: one versus two independently evolving lineages in Rhodnius ecuadoriensis
| Analyses and hypotheses | Pr(H) | Log-mL | SD | Log-BF | Pr(H|D)a |
|---|---|---|---|---|---|
| Nested sampling [69] | |||||
| H0: one lineage | 0.5 | − 3944.09 | 6.05 | 24.22 | 0 |
| H1: two lineages (“Ecuador” and “Peru”) | 0.5 | − 3919.87 | 5.59 | 0 | 1 |
| Path samplingb [70] | |||||
| H0: one lineage | 0.5 | − 3888.23 | – | 12.94 | < 0.00001 |
| H1: two lineages (“Ecuador” and “Peru”) | 0.5 | − 3875.29 | – | 0 | > 0.99999 |
Pr(H), Prior probability of each alternative hypothesis [here, both hypotheses are equally likely a priori: Pr(H0) = Pr(H1) = 0.5], Log-mL natural logarithm of the marginal likelihood, SD standard deviation of the log-mL, Log-BF natural logarithm of the Bayes factor (i.e. the difference in log-mL between H1 and H0), Pr(H|D) posterior probability of each hypothesis, given the data [here, Pr(H0|D) ≈ 0 and Pr(H1|D) ≈ 1 for both analyses]
aEstimated under the assumption of equal prior probabilities, as Pr(H1|D) ≈ BF/(1 + BF), and Pr(H0|D) = 1 − Pr(H1|D)
bOr “thermodynamic integration”; note that, in the implementation we used, this method does not provide SD estimates for the log-mLs