Bayesian cosmological inference through implicit cross-correlation
  statistics
  Analyzes of next-generation galaxy data require accurate treatment of
systematic effects such as the bias between observed galaxies and the
underlying matter density field. However, proposed models of the phenomenon are
either numerically expensive or too inaccurate to achieve unbiased inferences
of cosmological parameters even at mildly-nonlinear scales of the data. As an
alternative to constructing accurate galaxy bias models, requiring
understanding galaxy formation, we propose to construct likelihood
distributions for Bayesian forward modeling approaches that are insensitive to
linear, scale-dependent bias and provide robustness against model
misspecification. We use maximum entropy arguments to construct likelihood
distributions designed to account only for correlations between data and
inferred quantities. By design these correlations are insensitive to linear
galaxy biasing relations, providing the desired robustness. The method is
implemented and tested within a Markov Chain Monte Carlo approach. The method
is assessed using a halo mock catalog based on standard full, cosmological,
N-body simulations. We obtain unbiased and tight constraints on cosmological
parameters exploiting only linear cross-correlation rates for $k\le 0.10$
Mpc/h. Tests for halos of masses ~10$^{12}$ M$_\odot$ to ~10$^{13}$ M$_\odot$
indicate that it is possible to ignore all details of the linear, scale
dependent, bias function while obtaining robust constraints on cosmology. Our
results provide a promising path forward to analyzes of galaxy surveys without
the requirement of having to accurately model the details of galaxy biasing but
by designing robust likelihoods for the inference.
