Bayesian Deep Gaussian Processes for Correlated Functional Data: A Case Study in Power Spectra

Music City Center 

Understanding the structure of our universe and distribution of matter is an area of active research. As cosmological surveys grow, developing emulators to efficiently predict matter power spectra is essential. We are motivated by the Mira-Titan Universe simulation suite which, for a specified cosmological parameterization (i.e., a cosmology), provides multiple response curves of various fidelities, including correlated functional realizations. First, we estimate the underlying true matter power spectra, with appropriate uncertainty quantification (UQ), from all provided curves. We propose a Bayesian deep Gaussian process (DGP) hierarchical model which synthesizes all information and estimates the underlying matter power spectra, while providing effective UQ. Our model extends previous work on Bayesian DGPs from scalar responses to functional ones. Second, we leverage predicted power spectra from various cosmologies to accurately predict the matter power spectra for an unobserved cosmology. We leverage basis functions of the functional spectra to train a separate Gaussian process emulator. Our method performs well in synthetic exercises and against the benchmark emulator.

Deep Gaussian Processes

Hierarchical Modeling

Cosmology

Markov Chain Monte Carlo

Surrogate

Uncertainty Quanitification 

Astrostatistics Interest Group