Data from: Adaptive estimation for epidemic renewal and phylogenetic skyline models

Estimating temporal changes in a target population from phylogenetic or
count data is an important problem in ecology and epidemiology. Reliable
estimates can provide key insights into the climatic and biological
drivers influencing the diversity or structure of that population and
evidence hypotheses concerning its future growth or decline. In infectious
disease applications, the individuals infected across an epidemic form the
target population. The renewal model estimates the effective reproduction
number, R, of the epidemic from counts of observed incident cases. The
skyline model infers the effective population size, N, underlying a
phylogeny of sequences sampled from that epidemic. Practically, R measures
ongoing epidemic growth while N informs on historical caseload. While both
models solve distinct problems, the reliability of their estimates depends
on p-dimensional piecewise-constant functions. If p is misspecified, the
model might underfit significant changes or overfit noise and promote a
spurious understanding of the epidemic, which might misguide intervention
policies or misinform forecasts. Surprisingly, no transparent yet
principled approach for optimising p exists. Usually, p is heuristically
set, or obscurely controlled via complex algorithms. We present a
computable and interpretable p-selection method based on the minimum
description length (MDL) formalism of information theory. Unlike many
standard model selection techniques, MDL accounts for the additional
statistical complexity induced by how parameters interact. As a result,
our method optimises p so that R and N estimates properly and meaningfully
adapt to available data. It also outperforms comparable Akaike and
Bayesian information criteria on several classification problems, given
minimal knowledge of the parameter space, and exposes statistical
similarities among renewal, skyline and other models in biology. Rigorous
and interpretable model selection is necessary if trustworthy and
justifiable conclusions are to be drawn from piecewise models.