Uncertainty Quantification and Non‐Linear Bayesian Update of PCE Coefficients. Issue 1 (29th November 2013) - Litvinenko, Alexander; Matthies, Hermann G.
Abstract: The Bayesian Update is quite vital for uncertainty quantification. With BU we can take into account the given measurements of our physical model and update the a priori probability density function (which is very often far away from the truth) of the uncertain parameter. The standard full BU is based on sampling and sampling is not always acceptable or possible. In addition, it can require a very large number of samples and is expensive. This led to the development of sampling‐free Bayesian updates. We derive it from the variational problem associated with conditional expectation. Whereas the linear BU is a linear function of the prediction mismatch, here we used higher order polynomials. As an example we took the chaotic Lorenz 84 model. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)