Fall 2018

Hessian Matrix Inversion in 10^10 Dimensions with Parametric Bootstraps

Wednesday, Sep. 26, 2018 9:30 am10:00 am

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Uros Seljak (UC Berkeley)

A common statistical analysis problem is to determine the mean and the variance of a (few) parameter(s), marginalizing over a large number of latent variables, which are all correlated, so that the Hessian is a full rank matrix. This requires inverting the Hessian, which becomes impossible using linear algebra in a very high number of dimensions. I will present a method to obtain the Hessian inverse matrix elements using parametric bootstrap samples (simulations), where only a few samples already give a reliable estimate. I will present an application of this method to the cosmological data analysis problem, where we operate with up to 1010 fully correlated observations of galaxy positions, and we wish to determine a handful of cosmological parameters.