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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).