Physicist, Startup Founder, Blogger, Dad

Wednesday, September 30, 2009

Copula in cosmology?

A new paper co-authored by one of my collaborators: http://arxiv.org/abs/0909.5187

From Finance to Cosmology: The Copula of Large-Scale Structure

Robert J. Scherrer, Andreas A. Berlind, Qingqing Mao, Cameron K. McBride (Vanderbilt University)

Any multivariate distribution can be uniquely decomposed into marginal (1-point) distributions, and a function called the copula, which contains all of the information on correlations between the distributions. The copula provides an important new methodology for analyzing the density field in large-scale structure. We derive the empirical 2-point copula for the evolved dark matter density field. We find that this empirical copula is well-approximated by a Gaussian copula. We consider the possibility that the full n-point copula is also Gaussian and describe some of the consequences of this hypothesis. Future directions for investigation are discussed.

I don't understand the gravitational dynamics well enough to guess whether we should expect the dark matter distribution today to be described by Gaussian copula. The authors insert a number of caveats, referring to the use of copula to price mortgage securities :-)

See here for some correspondence with Scherrer on the topic of genius and modern science, and here for some popular coverage of the paper we wrote.

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