Choosing among Partition Models in Bayesian Phylogenetics

Abstract

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.

Multiple nuclear genes and retroposons support vicariance and dispersal of the palaeognaths, and an Early Cretaceous origin of modern birds

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Bayesian analysis of a morphological supermatrix sheds light on controversial fossil hominin relationships

“…Stepping-stone sampling [38,39] was used to estimate the marginal likelihoods of the tree models. In each 'step', MCMC was conducted for 196 000 generations and samples were taken every 1000 generations.…”

Assessing species boundaries and the phylogenetic position of the rare Szechwan ratsnake, Euprepiophis perlaceus (Serpentes: Colubridae), using coalescent-based methods

“…Since incorrect phylogenetic relationships in the guide tree will mislead the results supporting lineage splitting with high Pp, a fully resolved and correct guide tree is necessary (Leaché and Fujita, 2010). Thus, the other two tests using Brownie and BF model comparison, without constraining the tree topology a priori were also used and yield similar results to BP&P. For the BF model comparison approach, among multiple marginal likelihood estimators used for calculating the likelihood values including harmonic mean estimator (HME), the stabilized/smoothed harmonic mean estimator (sHME, Redelings and Suchard, 2005), path sampling (PS), and stepping-stone sampling (SS), HME and sHME (an extension of HME) have been demonstrated to perform poorly in choosing the correct model (Baele et al, 2012a,b;Fan et al, 2011;Xie et al, 2011). Specifically, a simulation study comparing the power of HME, sHME, PS and SS for the species model selection in * BEAST shows that only PS and SS estimators are sensitive in identifying the correct species model with both over splitting or lumping of lineages (Grummer et al, in press).…”