Kavli Affiliate: Salman Habib
| First 5 Authors: Kelly R. Moran, Richard Payne, Earl Lawrence, David Higdon, Stephen A. Walsh
| Summary:
The nonlinear matter power spectrum in cosmology describes how matter density
fluctuations vary with scale in the universe, providing critical insights into
large-scale structure formation. The matter power spectrum includes both smooth
regions and highly oscillatory features. Cosmologists rely on noisy,
multi-resolution realizations of large N-body simulations to study these
phenomena, which require appropriate smoothing techniques to learn about
underlying structures. We introduce a Bayesian Deep Process Convolution (DPC)
model that flexibly adapts its smoothness parameter across the input space,
enabling it to capture both smooth and variable structure within a single
framework. The DPC model leverages common patterns across related functions to
improve estimation in regions with sparse data. Compared to existing methods,
the DPC model offers superior accuracy and uncertainty quantification in
simulated data, and qualitatively superior performance with the cosmological
data. This methodology will be useful in cosmology and other fields requiring
flexible modeling of smooth nonstationary surfaces.
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