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Table 1 Mean 95% confidence or credible interval size with associated Type I error rate (true value outside interval), based on 3,000 simulated datasets

From: Bayesian models for comparative analysis integrating phylogenetic uncertainty

True σ 

Estimation method

 β  0

 β  1

 σ 

  

CI size

Error rate

CI size

Error rate

CI size

Error rate

2

Real GLS

6.12

0.002

0.23

0.121

1.74

1.000

 

True GLS

3.39

0.044

0.20

0.058

0.83

0.041

 

Bayes AT

3.26

0.057

0.20

0.063

0.86

0.037

 

Bayes OT

5.99

0.002

0.22

0.131

1.67

1.000

5

Real GLS

15.34

0.003

0.57

0.125

4.37

1.000

 

True GLS

8.50

0.057

0.49

0.059

2.07

0.050

 

Bayes AT

8.11

0.070

0.49

0.066

2.14

0.045

 

Bayes OT

15.02

0.003

0.56

0.133

4.18

1.000

10

Real GLS

30.43

0.003

1.14

0.115

8.66

1.000

 

True GLS

16.93

0.053

0.99

0.044

4.13

0.056

 

Bayes AT

16.16

0.069

0.99

0.056

4.27

0.051

 

Bayes OT

29.78

0.004

1.11

0.123

8.30

1.000

15

Real GLS

45.72

0.002

1.70

0.119

13.01

1.000

 

True GLS

25.36

0.051

1.46

0.054

6.19

0.051

 

Bayes AT

24.18

0.070

1.46

0.062

6.38

0.048

 

Bayes OT

44.72

0.003

1.66

0.128

12.47

1.000

  1. Simulated date were β0=5, β1=2 and several levels for σ parameter (see first column). Real GLS : Frequentist least-square using consensus tree; True GLS : Frequentist least-square using true phylogenetic tree; Bayes AT: Bayesian method using 100 trees (estimated from a real dataset) including the true tree; Bayes OT: Bayesian method using consensus tree. Marked error rate () are significantly different from expected 5% error rate (Binomial test, p<0.01).