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Activity Number: 477
Type: Invited
Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistics and the Environment
Abstract #310601
Title: Fast Bayesian Inference for Missing Data on Circular Domains
Author(s): Joe Guinness*+ and Montserrat Fuentes
Companies: North Carolina State University and North Carolina State University
Keywords: Big data ; Spatial statistics ; Likelihood approximation
Abstract:

When spatial data are observed at evenly spaced locations on a circular domain--such as a circle, torus, or a sphere--the resulting stationary covariance matrices have structure that can be exploited when computing Gaussian likelihoods. For example, if the domain is a circle, stationary covariance matrices are circulant and thus diagonizable by the discrete Fourier transform, so efficient computations of the log determinant and quadratic forms are possible with a fast Fourier transform algorithm. These computational benefits break down if some of the observations are missing. We present methods for efficiently imputing the missing values, and we describe how to perform inference on covariance parameters with a Gibbs sampler. The imputations rely on novel computational algorithms for solving linear systems that can be embedded inside of larger systems for which efficient matrix multiplications are possible. We extend these ideas to develop an alternative to the Whittle likelihood and suggest methods for analyzing irregularly-spaced data.


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