An adaptive significance threshold criterion for massive multiple hypotheses testing

This research deals with massive multiple hypothesis testing. First regarding multiple tests as an estimation problem under a proper population model, an error measurement called Erroneous Rejection Ratio (ERR) is introduced and related to the False Discovery Rate (FDR). ERR is an error measurement similar in spirit to FDR, and it greatly simplifies the analytical study of error properties of multiple test procedures. Next an improved estimator of the proportion of true null hypotheses and a data adaptive significance threshold criterion are developed. Some asymptotic error properties of the significant threshold criterion is established in terms of ERR under distributional assumptions widely satisfied in recent applications. A simulation study provides clear evidence that the proposed estimator of the proportion of true null hypotheses outperforms the existing estimators of this important parameter in massive multiple tests. Both analytical and simulation studies indicate that the proposed significance threshold criterion can provide a reasonable balance between the amounts of false positive and false negative errors, thereby complementing and extending the various FDR control procedures. S-plus/R code is available from the author upon request.Comment: Published at http://dx.doi.org/10.1214/074921706000000392 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Penguin-induced Radiative Baryonic B Decays Revisited

Weak radiative baryonic B decays $\bar B\to B_1\bar B_2\gamma$ mediated by the electromagnetic penguin process $b\to s\gamma$ are re-examined within the framework of the pole model. The meson pole contribution that has been neglected before is taken into account in this work. It is found that the intermediate $K^*$ contribution dominates in the $\Sigma\bar p\gamma$ mode and is comparable to the baryon pole effect in $\Lambda\bar p\gamma$ and $\Xi\bar\Lambda\gamma$ modes. The branching ratios for $B^-\to\Lambda\bar p\gamma$ and $B^-\to\Xi^0\bar\Sigma^-\gamma$ are of order $2.6\times 10^{-6}$ and $6\times 10^{-7}$, respectively. The threshold enhancement effect in the dibaryon mass spectrum is responsible by the meson pole diagram. We also study the angular distribution of the baryon in the dibaryon rest frame. The baryon pole diagrams imply that the antibaryon tends to emerge in the direction of the photon in the baryon-pair rest frame. The predicted angular asymmetry agrees with experiment for $B^-\to\Lambda\bar p\gamma$. Measurements of the correlation of the photon with the baryon allow us to discriminate between different models for describing the radiative baryonic B decays. For decays $B\to\Xi\bar\Sigma\gamma$, a large correlation of the photon to the $\bar\Sigma$ and a broad bump in the dibaryon mass spectrum are predicted.Comment: 10 pages, 4 figure

Collapsing strange quark matter in Vaidya geometry

Exact solutions of the gravitational field equations for a mixture of a null charged strange quark fluid and radiation are obtained in a Vaidya space-time. The conditions for the formation of a naked singularity are analyzed by considering the behavior of radial geodesics originating from the central singularity.Comment: 6 pages, no figure