# Hessian Matrix Inversion in 10^10 Dimensions with Parametric Bootstraps

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 10^{10} fully correlated observations of galaxy positions, and we wish to determine a handful of cosmological parameters.