What is it about?
We develop Bayesian update methods for solving coefficient inverse problems. Unknown coefficients in a PDE are considered as uncertain and are identified via the Bayesian formula. First, one guesses some prior distribution, then uses available measurements to compute the likelihood and the posterior distribution/density of the coefficients. The suggested method is a generalization of the famous Kalman filter update.
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Why is it important?
The inverse problem in Bayesian setting is a well-posed problem. Having the prior and the measurements, one can always compute the posterior. If available measurements are informative, then the posterior density will give more accurate statistical description (e.g, mean and variance) of the unknown coefficients.
Perspectives
This is a new research direction, which allows to incorporate available data into the model. One can speak about "data-driven" research. The offered method can be applied to non-Gaussian random fields/processes and is also non-linear (we speak about quadratic, cubic, etc Bayesian update). We apply this method for updating polynomial chaos coefficients.
Dr. Alexander Litvinenko
Rheinisch Westfalische Technische Hochschule Aachen
Read the Original
This page is a summary of: Inverse Problems in a Bayesian Setting, January 2016, Springer Science + Business Media,
DOI: 10.1007/978-3-319-27996-1_10.
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