Bayesian models for comparative analysis integrating phylogenetic uncertainty

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

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^∗

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).

ISSN: 2730-7182