Debiasing inference with approximate covariance matrices and other
  unidentified biases
  When a posterior peaks in unexpected regions of parameter space, new physics
has either been discovered, or a bias has not been identified yet. To tell
these two cases apart is of paramount importance. We therefore present a method
to indicate and mitigate unrecognized biases: Our method runs any pipeline with
possibly unknown biases on both simulations and real data. It computes the
coverage probability of posteriors, which measures whether posterior volume is
a faithful representation of probability or not. If found to be necessary, the
posterior is then corrected. This is a non-parametric debiasing procedure which
complies with objective Bayesian inference. We use the method to debias
inference with approximate covariance matrices and redshift uncertainties. We
demonstrate why approximate covariance matrices bias physical constraints, and
how this bias can be mitigated. We show that for a Euclid-like survey, if a
traditional likelihood exists, then 25 end-to-end simulations suffice to
guarantee that the figure of merit deteriorates maximally by 22 percent, or by
10 percent for 225 simulations. Thus, even a pessimistic analysis of
Euclid-like data will still constitute an 25-fold increase in precision on the
dark energy parameters in comparison to the state of the art (2018) set by KiDS
and DES. We provide a public code of our method.
