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We performed a meta-analysis of 14 genome-wide association studies of coronary artery disease (CAD) comprising 22,233 cases and 64,762 controls of European descent, followed by genotyping of top association signals in 60,738 additional individuals. This genomic analysis identified 13 novel loci harboring one or more SNPs that were associated with CAD at P<5×10−8 and confirmed the association of 10 of 12 previously reported CAD loci. The 13 novel loci displayed risk allele frequencies ranging from 0.13 to 0.91 and were associated with a 6 to 17 percent increase in the risk of CAD per allele. Notably, only three of the novel loci displayed significant association with traditional CAD risk factors, while the majority lie in gene regions not previously implicated in the pathogenesis of CAD. Finally, five of the novel CAD risk loci appear to have pleiotropic effects, showing strong association with various other human diseases or traits.

A theory for estimating the probability distribution of the state of a model given a set of observations exists. This nonlinear filtering theory unifies the data assimilation and ensemble generation problem that have been key foci of prediction and predictability research for numerical weather and ocean prediction applications. A new algorithm, referred to as an ensemble adjustment Kalman filter, and the more traditional implementation of the ensemble Kalman filter in which ''perturbed observations'' are used, are derived as Monte Carlo approximations to the nonlinear filter. Both ensemble Kalman filter methods produce assimilations with small ensemble mean errors while providing reasonable measures of uncertainty in the assimilated variables. The ensemble methods can assimilate observations with a nonlinear relation to model state variables and can also use observations to estimate the value of imprecisely known model parameters. These ensemble filter methods are shown to have significant advantages over four-dimensional variational assimilation in low-order models and scale easily to much larger applications. Heuristic modifications to the filtering algorithms allow them to be applied efficiently to very large models by sequentially processing observations and computing the impact of each observation on each state variable in an independent calculation. The ensemble adjustment Kalman filter is applied to a nondivergent barotropic model on the sphere to demonstrate the capabilities of the filters in models with state spaces that are much larger than the ensemble size. When observations are assimilated in the traditional ensemble Kalman filter, the resulting updated ensemble has a mean that is consistent with the value given by filtering theory, but only the expected value of the covariance of the updated ensemble is consistent with the theory. The ensemble adjustment Kalman filter computes a linear operator that is applied to the prior ensemble estimate of the state, resulting in an updated ensemble whose mean and also covariance are consistent with the theory. In the cases compared here, the ensemble adjustment Kalman filter performs significantly better than the traditional ensemble Kalman filter, apparently because noise introduced into the assimilated ensemble through perturbed observations in the traditional filter limits its relative performance. This superior performance may not occur for all problems and is expected to be most notable for small ensembles. Still, the results suggest that careful study of the capabilities of different varieties of ensemble Kalman filters is appropriate when exploring new applications.

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