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.
Description
Cosmic Inference: Constraining Parameters With Observations and Highly Limited Number of Simulations
%0 Generic
%1 takhtaganov2019cosmic
%A Takhtaganov, Timur
%A Lukic, Zarija
%A Mueller, Juliane
%A Morozov, Dmitriy
%D 2019
%K library
%T Cosmic Inference: Constraining Parameters With Observations and Highly
Limited Number of Simulations
%U http://arxiv.org/abs/1905.07410
%X 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.
@misc{takhtaganov2019cosmic,
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.},
added-at = {2019-05-21T04:09:59.000+0200},
author = {Takhtaganov, Timur and Lukic, Zarija and Mueller, Juliane and Morozov, Dmitriy},
biburl = {https://www.bibsonomy.org/bibtex/2885fb6cfd51a173e791a5011aef256b4/gpkulkarni},
description = {Cosmic Inference: Constraining Parameters With Observations and Highly Limited Number of Simulations},
interhash = {270fc7af4338fdd3e1ec73e47b252b32},
intrahash = {885fb6cfd51a173e791a5011aef256b4},
keywords = {library},
note = {cite arxiv:1905.07410Comment: 23 pages, 17 figures, submitted to ApJ},
timestamp = {2019-05-21T04:09:59.000+0200},
title = {Cosmic Inference: Constraining Parameters With Observations and Highly
Limited Number of Simulations},
url = {http://arxiv.org/abs/1905.07410},
year = 2019
}