A Gaussian-mixture ensemble transform filter

We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions. Copyright © 2011 Royal Meteorological Society

Correlation of the highest-energy cosmic rays with the positions of nearby active galactic nuclei

Data collected by the Pierre Auger Observatory provide evidence for anisotropy in the arrival directions of the cosmic rays with the highest-energies, which are correlated with the positions of relatively nearby active galactic nuclei (AGN) [Pierre Auger Collaboration, Science 318 (2007) 938]. The correlation has maximum significance for cosmic rays with energy greater than similar to 6 x 10(19) eV and AGN at a distance less than similar to 75 Mpc. We have confirmed the anisotropy at a confidence level of more than 99% through a test with parameters specified a priori, using an independent data set. The observed correlation is compatible with the hypothesis that cosmic rays with the highest-energies originate from extra-galactic sources close enough so that their flux is not significantly attenuated by interaction with the cosmic background radiation (the Greisen-Zatsepin-Kuz`min effect). The angular scale of the correlation observed is a few degrees, which suggests a predominantly light composition unless the magnetic fields are very weak outside the thin disk of our galaxy. Our present data do not identify AGN as the sources of cosmic rays unambiguously, and other candidate sources which are distributed as nearby AGN are not ruled out. We discuss the prospect of unequivocal identification of individual sources of the highest-energy cosmic rays within a few years of continued operation of the Pierre Auger Observatory. (C) 2008 Elsevier B.V. All rights reserved.