Statistical Treatment of inverse problems constrained by differential equations-based models with stochastic terms: Neyman Seminar

Seminar | December 4 | 4-5 p.m. | 1011 Evans Hall

 Noemi Petra, UC Merced

 Department of Statistics

In this talk, we introduce a statistical treatment of
inverse problems constrained by models with stochastic terms. The
solution of the forward problem is given by a distribution represented
numerically by an ensemble of simulations. The goal is to formulate
the inverse problem, in particular the objective function, to find the
closest forward distribution (i.e., the output of the stochastic
forward problem) that best explains the distribution of the
observations in a certain metric. We use proper scoring rules, a
concept employed in statistical forecast verification, namely energy,
variogram, and hybrid (i.e., combination of the two) scores. We study
the performance of the proposed formulation in the context of two
applications: a coefficient field inversion for subsurface flow
governed by an elliptic partial differential equation with a
stochastic source and a parameter inversion for power grid governed
by differential-algebraic equations. In both cases we show that the
variogram and the hybrid scores produce better parameter inversion
results than does the energy score, whereas the energy score leads to
better probabilistic predictions.

 Berkeley, CA 94720, 5106422781