Cosmic Inference: Constraining Parameters with Observations and a Highly Limited Number of Simulations

Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and objective to infer values of model parameters that characterize underlying physical system—our universe, from these observations theoretical forward-modeling. The only way accurately forward-model behavior on small scales via expensive numerical simulations, which are further "emulated" due their high cost. Emulators commonly built with a set simulations covering parameter space Latin hypercube sampling interpolation procedure; aim establish approximately constant prediction error across hypercube. In this paper, we provide description novel statistical framework for obtaining accurate constraints. proposed uses multi-output Gaussian process emulators adaptively constructed using Bayesian optimization methods goal maintaining low emulation in region preferred by observational data. compare several approaches constructing enable us take possible inter-output correlations into account while efficiency needed inference. Using Ly? forest flux power spectrum, demonstrate our adaptive approach requires considerably fewer—by factor few P(k) case considered here—simulations compared based sampling, method more robust reconstructing credible intervals.