| Abstract: |
| This talk will describe recent work on two different geophysical problems which we formulate as a Bayesian statistical inverse problem. The first problem concerns the estimation of a velocity field u from sparse observations of a scalar $\theta$, e.g. concentration of a solute, passively advected and diffusing in the fluid medium. The second problem concerns the usage of historical records to provide improved understanding of a series of seismic events which produced Tsunamis in the Indonesian basin. Beyond the inherent interest for applications, these two problems raise theoretical questions of broader statistical, computational and mathematical interest. We will present results concerning consistency and describe some novel Markov Chain Monte Carlo (MCMC) algorithms to effectively sample from classes of infinite dimensional probability measures as arise in our examples. |
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