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Table 3 Marginal likelihoods, Bayes factors and hypothesis testing: one versus two independently evolving lineages in Rhodnius ecuadoriensis

From: Under pressure: phenotypic divergence and convergence associated with microhabitat adaptations in Triatominae

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

  1. 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]
  2. aEstimated under the assumption of equal prior probabilities, as Pr(H1|D) ≈ BF/(1 + BF), and Pr(H0|D) = 1 − Pr(H1|D)
  3. bOr “thermodynamic integration”; note that, in the implementation we used, this method does not provide SD estimates for the log-mLs