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Optimal Transport Driven Bayesian Inversion With Application To Signal Processing, Elijah F. Perez
Optimal Transport Driven Bayesian Inversion With Application To Signal Processing, Elijah F. Perez
Mathematics & Statistics ETDs
This paper will outline a Debiased Sinkhorn Divergence driven Bayesian inversion framework. Conventionally, a Gaussian Driven Bayesian framework is used when performing Bayesian inversion. A major issue with this Gaussian framework is that the Gaussian likelihood, driven by the L2 norm, is not affected by phase shift in a given signal. This issue has been addressed in [1] using a Wasserstein framework. However, the Wasserstein framework still has an issue because it assumes statistical independence when multidimensional signals are analyzed. This assumption of statistical independence cannot always be made when analyzing signals where multiple detectors are recording one event, say …
Deterministic And Probabilistic Methods For Seismic Source Inversion, Juan Pablo Madrigal Cianci
Deterministic And Probabilistic Methods For Seismic Source Inversion, Juan Pablo Madrigal Cianci
Mathematics & Statistics ETDs
The national Earthquake Information Center (NEIC) reports an occurrence of about 13,000 earthquakes every year, spanning different values on the Richter scale from very mild (2) to "giant earthquakes'' (8 and above). Being able to study these earthquakes provides useful information for a wide range of applications in geophysics. In the present work we study the characteristics of an earthquake by performing seismic source inversion; a mathematical problem that, given some recorded data, produces a set of parameters that when used as input in a mathematical model for the earthquake generates synthetic data that closely resembles the measured data. There …