Cosmic Inference: Constraining Parameters With Observations and Highly Limited Number of Simulations (1905.07410v1)

Abstract: Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters which characterize the underlying physical system -- our Universe. Modern cosmological probes increasingly rely on measurements of the small-scale structure, and the only way to accurately model physical behavior on those scales, roughly 65 Mpc/h or smaller, is via expensive numerical simulations. In this paper, we provide a detailed description of a novel statistical framework for obtaining accurate parameter constraints by combining observations with a very limited number of cosmological simulations. The proposed framework utilizes multi-output Gaussian process emulators that are adaptively constructed using Bayesian optimization methods. We compare several approaches for constructing multi-output emulators that enable us to take possible inter-output correlations into account while maintaining the efficiency needed for inference. Using Lyman alpha forest flux power spectrum, we demonstrate that our adaptive approach requires considerably fewer --- by a factor of a few in Lyman alpha P(k) case considered here --- simulations compared to the emulation based on Latin hypercube sampling, and that the method is more robust in reconstructing parameters and their Bayesian credible intervals.