Kriging Interpolating Cosmic Velocity Field

[abridged] Volume-weighted statistics of large scale peculiar velocity is preferred by peculiar velocity cosmology, since it is free of uncertainties of galaxy density bias entangled in mass-weighted statistics. However, measuring the volume-weighted velocity statistics from galaxy (halo/simulation particle) velocity data is challenging. For the first time, we apply the Kriging interpolation to obtain the volume-weighted velocity field. Kriging is a minimum variance estimator. It predicts the most likely velocity for each place based on the velocity at other places. We test the performance of Kriging quantified by the E-mode velocity power spectrum from simulations. Dependences on the variogram prior used in Kriging, the number $n_k$ of the nearby particles to interpolate and the density $n_P$ of the observed sample are investigated. First, we find that Kriging induces $1\%$ and $3\%$ systematics at $k\sim 0.1h{\rm Mpc}^{-1}$ when $n_P\sim 6\times 10^{-2} ({\rm Mpc}/h)^{-3}$ and $n_P\sim 6\times 10^{-3} ({\rm Mpc}/h)^{-3}$, respectively. The deviation increases for decreasing $n_P$ and increasing $k$. When $n_P\lesssim 6\times 10^{-4} ({\rm Mpc}/h)^{-3}$, a smoothing effect dominates small scales, causing significant underestimation of the velocity power spectrum. Second, increasing $n_k$ helps to recover small scale power. However, for $n_P\lesssim 6\times 10^{-4} ({\rm Mpc}/h)^{-3}$ cases, the recovery is limited. Finally, Kriging is more sensitive to the variogram prior for lower sample density. The most straightforward application of Kriging on the cosmic velocity field does not show obvious advantages over the nearest-particle method (Zheng et al. 2013) and could not be directly applied to cosmology so far. However, whether potential improvements may be achieved by more delicate versions of Kriging is worth further investigation.Comment: 11 pages, 5 figures, published in PR

Block-based Bayesian epistasis association mapping with application to WTCCC type 1 diabetes data

Interactions among multiple genes across the genome may contribute to the risks of many complex human diseases. Whole-genome single nucleotide polymorphisms (SNPs) data collected for many thousands of SNP markers from thousands of individuals under the case–control design promise to shed light on our understanding of such interactions. However, nearby SNPs are highly correlated due to linkage disequilibrium (LD) and the number of possible interactions is too large for exhaustive evaluation. We propose a novel Bayesian method for simultaneously partitioning SNPs into LD-blocks and selecting SNPs within blocks that are associated with the disease, either individually or interactively with other SNPs. When applied to homogeneous population data, the method gives posterior probabilities for LD-block boundaries, which not only result in accurate block partitions of SNPs, but also provide measures of partition uncertainty. When applied to case–control data for association mapping, the method implicitly filters out SNP associations created merely by LD with disease loci within the same blocks. Simulation study showed that this approach is more powerful in detecting multi-locus associations than other methods we tested, including one of ours. When applied to the WTCCC type 1 diabetes data, the method identified many previously known T1D associated genes, including PTPN22, CTLA4, MHC, and IL2RA. The method also revealed some interesting two-way associations that are undetected by single SNP methods. Most of the significant associations are located within the MHC region. Our analysis showed that the MHC SNPs form long-distance joint associations over several known recombination hotspots. By controlling the haplotypes of the MHC class II region, we identified additional associations in both MHC class I (HLA-A, HLA-B) and class III regions (BAT1). We also observed significant interactions between genes PRSS16, ZNF184 in the extended MHC region and the MHC class II genes. The proposed method can be broadly applied to the classification problem with correlated discrete covariates.Statistic