Bayesian Control Variates for optimal covariance estimation with pairs of simulations and surrogates

Understand

Predictions of the mean and covariance matrix of summary statistics are critical for confronting cosmological theories with observations, not least for likelihood approximations and parameter inference.

• The price to pay for accurate estimates is the extreme cost of running $N$-body and hydrodynamics simulations.
• Approximate solvers, or surrogates, greatly reduce the computational cost but can introduce significant biases, for example in the non-linear regime of cosmic structure growth.
• We propose "CARPool Bayes", an approach to solve the inference problem for both the means and covariances using a combination of simulations and surrogates.