Bayesian methods to overcome the winner's curse in genetic studies

Parameter estimates for associated genetic variants, report ed in the initial discovery samples, are often grossly inflated compared to the values observed in the follow-up replication samples. This type of bias is a consequence of the sequential procedure in which the estimated effect of an associated genetic marker must first pass a stringent significance threshold. We propose a hierarchical Bayes method in which a spike-and-slab prior is used to account for the possibility that the significant test result may be due to chance. We examine the robustness of the method using different priors corresponding to different degrees of confidence in the testing results and propose a Bayesian model averaging procedure to combine estimates produced by different models. The Bayesian estimators yield smaller variance compared to the conditional likelihood estimator and outperform the latter in studies with low power. We investigate the performance of the method with simulations and applications to four real data examples.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS373 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra

We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions $\leq 11$. For dimensions $D=10,11$ we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry algebra.Comment: New version with some additions and correction

Can the age discrepancies of neutron stars be circumvented by an accretion-assisted torque?

It is found that 1E 1207.4-5209 could be a low-mass bare strange star if its small radius or low altitude cyclotron formation can be identified. The age problems of five sources could be solved by a fossil-disk-assisted torque. The magnetic dipole radiation dominates the evolution of PSR B1757-24 at present, and the others are in propeller (or tracking) phases.Comment: ApJL accepted, or at http://vega.bac.pku.edu.cn/~rxxu/publications/index_P.ht