Choosing among partition models in Bayesian phylogenetics.
Bayesian phylogenetic analyses often depend on Bayes factors (BFs) to determine the optimal way to partition the data. The marginal likelihoods used to compute BFs, in turn, are most commonly estimated using the harmonic mean (HM) method, which has been shown to be inaccurate. We describe a new more accurate method for estimating the marginal likelihood of a model and compare it with the HM method on both simulated and empirical data. The new method generalizes our previously described stepping-stone (SS) approach by making use of a reference distribution parameterized using samples from the posterior distribution. This avoids one challenging aspect of the original SS method, namely the need to sample from distributions that are close (in the Kullback-Leibler sense) to the prior. We specifically address the choice of partition models and find that using the HM method can lead to a strong preference for an overpartitioned model. In contrast to the HM method and the original SS method, we show using simulated data that the generalized SS method is strikingly more precise (repeatable BF values of the same data and partition model) and yields BF values that are much more reasonable than those produced by the HM method. Comparisons of HM and generalized SS methods on an empirical data set demonstrate that the generalized SS method tends to choose simpler partition schemes that are more in line with expectation based on inferred patterns of molecular evolution. The generalized SS method shares with thermodynamic integration the need to sample from a series of distributions in addition to the posterior. Such dedicated path-based Markov chain Monte Carlo analyses appear to be a cost of estimating marginal likelihoods accurately.
Fan
Yu
Y
Department of Ecology and Evolutionary Biology, University of Connecticut.
Wu
Rui
R
Chen
Ming-Hui
MH
Kuo
Lynn
L
Lewis
Paul O
PO
D001499:Bayes Theorem; D019143:Evolution, Molecular; D008390:Markov Chains; D008957:Models, Genetic; D009010:Monte Carlo Method; D010802:Phylogeny
Mol Biol Evol. 2004 Jun;21(6):1123-33
15034130
Syst Biol. 2011 Mar;60(2):150-60
21187451
Mol Biol Evol. 2009 Dec;26(12):2699-709
19692665
Syst Biol. 2015 May;64(3):525-31
25577605
Syst Biol. 2008 Apr;57(2):185-201
18404577
Syst Biol. 2006 Apr;55(2):195-207
16522570
Bioinformatics. 2003 Aug 12;19(12):1572-4
12912839
Syst Biol. 2010 Jan;59(1):108-17
20525623
Syst Biol. 2007 Dec;56(6):975-87
18075934
Syst Biol. 2005 Jun;54(3):373-90
16012105
Syst Biol. 2007 Aug;56(4):643-55
17661232
Syst Biol. 2006 Dec;55(6):993-1003
17345679
Mol Biol Evol. 2001 Jun;18(6):1001-13
11371589
Syst Biol. 2004 Feb;53(1):47-67
14965900
Mol Biol Evol. 2010 Jan;27(1):161-76
19762334
Comput Appl Biosci. 1997 Jun;13(3):235-8
9183526