M. Peters (ETH Zürich)
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We discuss several numerical aspects of uncertainty quantification in elliptic partial differential equations. 
We begin by representing random data in terms of a Karhunen-Loeve expansion.
The latter can be computed efficiently by the pivoted Cholesky decomposition. 
Having this representation at hand, the computation of statistics of the system response leads to 
high dimensional quadrature problems which we address by the anisotropic sparse quadrature. 
Finally, we show how to incorporate measurement data into our model by means of
Bayesian inversion.