Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters that characterize the underlying physical system—our universe, from these observations and theoretical forward-modeling. The only way to accurately forward-model physical behavior on small scales is via expensive numerical simulations, which are further “emulated” due to their high cost. Emulators are commonly built with a set of simulations covering the parameter space with Latin hypercube sampling and an interpolation procedure; the aim is to establish an approximately constant prediction error across the hypercube. In this paper, we provide a description of a novel statistical framework for obtaining accurate parameter constraints. The proposed framework uses multi-output Gaussian process emulators that are adaptively constructed using Bayesian optimization methods with the goal of maintaining a low emulation error in the region of the hypercube preferred by the observational data. In this paper, 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 a Lyα forest flux power spectrum, we demonstrate that our adaptive approach requires considerably fewer—by a factor of a few in the Lyα 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.
We present an adaptive approach to the construction of Gaussian process surrogates for Bayesian inference with expensive-to-evaluate forward models. Our method relies on the fully Bayesian approach to training Gaussian process models and utilizes the expected improvement idea from Bayesian global optimization. We adaptively construct training designs by maximizing the expected improvement in fit of the Gaussian process model to the noisy observational data. Numerical experiments on model problems with synthetic data demonstrate the effectiveness of the obtained adaptive designs compared to the fixed non-adaptive designs in terms of accurate posterior estimation at a fraction of the cost of inference with forward models.
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, x 65 h −1 Mpc, 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-α forest flux power spectrum, we demonstrate that our adaptive approach requires considerably fewer -by a factor of a few in Lyman-α 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.
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