Simulation-Aided Inference in Cosmology

In this paper we describe two Bayesian statistical approaches for combining large-scale computational models with physical observations to make inferences about cosmological parameters. The first method is a Bayesian calibration approach adapted from Kennedy and O’Hagan (J R Stat Soc B 68:425–464, 2001) and Higdon et al. (J Am Stat Assoc 103:570–583, 2008). It makes use of a response surface model that approximates the simulation output at untried input settings. The second approach uses the ensemble Kalman filter (Evensen, IEEE Control Syst Mag 29:83–104, 2009), which makes use of an ensemble of simulations and physical observations to update the prior parameter distribution using standard equations from Kalman filtering. We apply these methods to large-scale structure simulations and observations from the Sloan Digital Sky Survey.