156 research outputs found
Stochastic approximation of score functions for Gaussian processes
We discuss the statistical properties of a recently introduced unbiased
stochastic approximation to the score equations for maximum likelihood
calculation for Gaussian processes. Under certain conditions, including bounded
condition number of the covariance matrix, the approach achieves storage
and nearly computational effort per optimization step, where is the
number of data sites. Here, we prove that if the condition number of the
covariance matrix is bounded, then the approximate score equations are nearly
optimal in a well-defined sense. Therefore, not only is the approximation
efficient to compute, but it also has comparable statistical properties to the
exact maximum likelihood estimates. We discuss a modification of the stochastic
approximation in which design elements of the stochastic terms mimic patterns
from a factorial design. We prove these designs are always at least as
good as the unstructured design, and we demonstrate through simulation that
they can produce a substantial improvement over random designs. Our findings
are validated by numerical experiments on simulated data sets of up to 1
million observations. We apply the approach to fit a space-time model to over
80,000 observations of total column ozone contained in the latitude band
-N during April 2012.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS627 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Convergence Analysis of Fixed Point Chance Constrained Optimal Power Flow Problems
For optimal power flow problems with chance constraints, a particularly
effective method is based on a fixed point iteration applied to a sequence of
deterministic power flow problems. However, a priori, the convergence of such
an approach is not necessarily guaranteed. This article analyses the
convergence conditions for this fixed point approach, and reports numerical
experiments including for large IEEE networks
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