Are skyline plot-based demographic estimates overly dependent on smoothing prior assumptions?

In Bayesian phylogenetics, the coalescent process provides an informative framework for inferring dynamical changes in the effective size of a population from a sampled phylogeny (or tree) of its sequences. Popular coalescent inference methods such as the Bayesian Skyline Plot, Skyride and Skygrid all model this population size with a discontinuous, piecewise-constant likelihood but apply a smoothing prior to ensure that posterior population size estimates transition gradually with time. These prior distributions implicitly encode extra population size information that is not available from the observed coalescent tree (data). Here we present a novel statistic, Ω, to quantify and disaggregate the relative contributions of the coalescent data and prior assumptions to the resulting posterior estimate precision. Our statistic also measures the additional mutual information introduced by such priors. Using Ω we show that, because it is surprisingly easy to over-parametrise piecewise-constant population models, common smoothing priors can lead to overconfident and potentially misleading conclusions, even under robust experimental designs. We propose Ω as a useful tool for detecting when posterior estimate precision is overly reliant on prior choices