Adaptive parallel tempering for BEAST 2

With ever more complex models used to study evolutionary patterns, approaches that facilitate efficient inference under such models are needed. Parallel tempering has long been used to speed up phylogenetic analyses and to make use of multi-core CPUs. Parallel tempering essentially runs multiple MCMC chains in parallel. All chains are heated except for one cold chain that explores the posterior probability space like a regular MCMC chain. This heating allows chains to make bigger jumps in phylogenetic state space. The heated chains can then be used to propose new states for other chains, including the cold chain. One of the practical challenges using this approach, is to find optimal temperatures of the heated chains to efficiently explore state spaces. We here provide an adaptive parallel tempering scheme to Bayesian phylogenetics, where the temperature difference between heated chains is automatically tuned to achieve a target acceptance probability of states being exchanged between individual chains. We first show the validity of this approach by comparing inferences of adaptive parallel tempering to MCMC on several datasets. We then explore where parallel tempering provides benefits over MCMC. We implemented this adaptive parallel tempering approach as an open source package licensed under GPL 3.0 to the Bayesian phylogenetics software BEAST2, available from https://github.com/nicfel/CoupledMCMC.