Recommendations for using msBayes to incorporate uncertainty in selecting an abc model prior: a response to oaks et Al.

Prior specification is an essential component of parameter estimation and model comparison in Approximate Bayesian computation (ABC). Oaks et al. present a simulation-based power analysis of msBayes and conclude that msBayes has low power to detect genuinely random divergence times across taxa, and suggest the cause is Lindley's paradox. Although the predictions are similar, we show that their findings are more fundamentally explained by insufficient prior sampling that arises with poorly chosen wide priors that critically undersample nonsimultaneous divergence histories of high likelihood. In a reanalysis of their data on Philippine Island vertebrates, we show how this problem can be circumvented by expanding upon a previously developed procedure that accommodates uncertainty in prior selection using Bayesian model averaging. When these procedures are used, msBayes supports recent divergences without support for synchronous divergence in the Oaks et al. data and we further present a simulation analysis that demonstrates that msBayes can have high power to detect asynchronous divergence under narrower priors for divergence time. Our findings highlight the need for exploration of plausible parameter space and prior sampling efficiency for ABC samplers in high dimensions. We discus potential improvements to msBayes and conclude that when used appropriately with model averaging, msBayes remains an effective and powerful tool.