Improved spectral estimation of equatorial spreadFthrough aperiodic pulsing and Bayesian inversion

Spectral Triples and Aperiodic Order

We construct spectral triples for compact metric spaces (X, d). This provides us with a new metric d̄s on X. We study its relation with the original metric d. When X is a subshift space, or a discrete tiling space, and d satisfies certain bounds we advocate that the property of d̄s and d to be Lipschitz equivalent is a characterization of high order. For episturmian subshifts, we prove that d̄s an...

Computational aspects of Bayesian spectral density estimation

Gaussian time-series models are often specified through their spectral density. Such models pose several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of the likelihood for such models. We use importance sampling to correct for the approximation error. We show that the variance of the importance sampling weights...

Spectral Notions of Aperiodic Order

Various spectral notions have been employed to grasp the structure of point sets, in particular non-periodic ones. In this article, we present them in a unified setting and explain the relations between them. For the sake of readability, we use Delone sets in Euclidean space as our main object class, and give generalisations in the form of further examples and remarks.

Parameter estimation via conditional expectation: a Bayesian inversion

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp. functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by actual observations of the response of the real system. In a probabilistic setting, Bayes’s theory is the proper mathematical background for this identification pr...

Bayesian Ambient Noise Inversion for Geoacoustic Uncertainty Estimation: Final report