LAUSR

The authors present an attractive solution to a long-standing problem of local adaptivity of Gaussian process priors for phylodynamic inference. While Gaussian process–based phylodynamics have been used for over 10 years (Minin et al., 2008; Gill et al., 2013; Palacios and Minin, 2013), these methods a priori assume a single precision parameter that controls smoothness over the whole population size history, limiting precision of posterior estimates in cases of variable smoothness over time or abrupt changes. The authors propose a horseshoe Markov random field (HSMRF) prior of order p on the log-effective population size trajectory at a regular fixed grid of H + 1 time points. The HSMRF is flexible to local adaptivity modeling each pth-order forward difference of the logtrajectory with a prior that spikes at 0 with Cauchy-like heavy tails. The HSMRF favors small variance of small population size jumps and large variance of large population size jumps. We discuss two aspects of the proposed method: (a) posterior checks and model selection that can accompany HSMRF modeling tools, and (b) the ability of the HSMRF model to differentiate between alternative population size trajectories that can be translated into meaningful scientific discoveries. In this discussion, we assume the inference setting in which a genealogy is observed.