Nonstationary Random Fields: Applications and Theory

• Activity Number: 596
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Ethan Anderes*+
• Companies: University of California at Davis
• Keywords: nonstationary random fields ; cosmic microwave background ; infill asymptotics

Abstract

In this talk we discuss some recent developments in the theory and application of nonstationary random fields. We will focus on classes of random field models which can generate spatially varying local sheer. These are applied to the problem of estimating dark matter density from observed cosmic microwave background intensity and polarization fields. In this example one can use Bayesian techniques to estimate the average curvature of the lensing gravitational potential over small local regions. These local curvatures are then used to construct an estimate of a low pass filter of the projected dark matter density. By utilizing Bayesian/likelihood methods one can easily overcome problems with missing and/or non-uniform pixels and problems with partial sky observations (E and B mode mixing, for example). Moreover, our methods are local in nature which allow us to easily model spatially varying beams and are highly parallelizable. We finish with some recent infill asymptotic results for random fields and their relevance to application.