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

In Bayesian phylogenetics, the coalescent process provides an informative
framework for inferring changes in the effective size of a population from
a phylogeny (or tree) of sequences sampled from that population. Popular
coalescent inference approaches such as the Bayesian Skyline Plot, Skyride
and Skygrid all model these population size changes with a discontinuous,
piecewise-constant function but then apply a smoothing prior to ensure
that their 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 data i.e.
the tree. 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 inference, even under robust
experimental designs. We propose Ω as a useful tool for detecting when
posterior estimate precision is overly reliant on prior choices.