Constructing Exponential Family Approximations to Cosmological Models

• Activity Number: 377
• Type: Invited
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Chad Michael Schafer*+
• Companies: Carnegie Mellon University
• Keywords: astronomy ; physical models ; exponential families

Abstract

A recurring challenge in astrostatistics is the need to estimate physical constants in cases where the complexity of the relationship between the parameters of interest and the distribution of the observable data is such that a standard likelihood-based approach will not be feasible. This talk will describe a method for fitting an approximation to an exponential family to a cosmological model. The result of the fit is both a set of sufficient statistics and a natural parameterization for the model. This approximate model could then be used as part of, for example, an implementation of MCMC or Approximate Bayesian Computation (ABC) approaches. The fitting is done on simulated data, hence this approach will require the ability to forward simulate the physical process that generates the data; fortunately, theoretical knowledge has made this is an increasingly common circumstance in astronomy.