  While Bayesian inference techniques are standard in cosmological analyses, it
is common to interpret resulting parameter constraints with a frequentist
intuition. This intuition can fail, e.g. when marginalizing high-dimensional
parameter spaces onto subsets of parameters, because of what has come to be
known as projection effects or prior volume effects. We present the method of
Informed Total-Error-Minimizing (ITEM) priors to address this. An ITEM prior is
a prior distribution on a set of nuisance parameters, e.g. ones describing
astrophysical or calibration systematics, intended to enforce the validity of a
frequentist interpretation of the posterior constraints derived for a set of
target parameters, e.g. cosmological parameters. Our method works as follows:
For a set of plausible nuisance realizations, we generate target parameter
posteriors using several different candidate priors for the nuisance
parameters. We reject candidate priors that do not accomplish the minimum
requirements of bias (of point estimates) and coverage (of confidence regions
among a set of noisy realizations of the data) for the target parameters on one
or more of the plausible nuisance realizations. Of the priors that survive this
cut we select the ITEM prior as the one that minimizes the total error of the
marginalized posteriors of the target parameters. As a proof of concept, we
apply our method to the Density Split Statistics (DSS) measured in Dark Energy
Survey Year 1 data. We demonstrate that the ITEM priors substantially reduce
prior volume effects that otherwise arise and allow sharpened yet robust
constraints on the parameters of interest.
