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arXiv 1106.0322stat.APstat.CO
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基于广义t先验的遗传关联信号贝叶斯稀疏路径分析

Bayesian Sparsity-Path-Analysis of Genetic Association Signal using Generalized t Priors

Anthony Lee, Francois Caron, Arnaud Doucet, Chris Holmes

摘要:

我们探索使用广义t先验的回归系数,以帮助理解关联信号的性质内的“命中区域”的全基因组关联研究。我们采用的特殊广义t分布是关于其辐角绝对值的学生分布。对于低自由度,我们表明,广义t表现出“稀疏先验”的性质与其他常见形式的稀疏先验的一些有吸引力的功能,包括众所周知的双指数分布的自由度趋于无穷大。我们特别注意从稀疏路径分析(SPA)中获得的后验统计数据的图形表示,在SPA中,我们扫过尺度的设置(收缩/精度)参数,以探索在一系列复杂性上获得的后验模型的空间,从所有系数分布严重集中在零附近的非常稀疏的模型,扩散先验和系数分布在其最大似然估计周围的模型。SPA图类似于最大后验(MAP)估计的LASSO图,但它们将绘制的系数的完整边缘后验分布作为先验精度的函数。在一定范围的先验精度上生成后验分布在计算上是具有挑战性的,但自然服从于以尺度参数为索引的序贯蒙特卡罗(SMC)算法。我们展示了如何SMC模拟图形处理单元(GPU)提供了非常有效的推理SPA。我们还提出了一个规模的混合表示的广义t前,导致期望最大化算法,以获得MAP估计应该只需要这些。

英文摘要:

We explore the use of generalized t priors on regression coefficients to help understand the nature of association signal within "hit regions" of genome-wide association studies. The particular generalized t distribution we adopt is a Student distribution on the absolute value of its argument. For low degrees of freedom we show that the generalized t exhibits 'sparsity-prior' properties with some attractive features over other common forms of sparse priors and includes the well known double-exponential distribution as the degrees of freedom tends to infinity. We pay particular attention to graphical representations of posterior statistics obtained from sparsity-path-analysis (SPA) where we sweep over the setting of the scale (shrinkage / precision) parameter in the prior to explore the space of posterior models obtained over a range of complexities, from very sparse models with all coefficient distributions heavily concentrated around zero, to models with diffuse priors and coefficients distributed around their maximum likelihood estimates. The SPA plots are akin to LASSO plots of maximum a posteriori (MAP) estimates but they characterise the complete marginal posterior distributions of the coefficients plotted as a function of the precision of the prior. Generating posterior distributions over a range of prior precisions is computationally challenging but naturally amenable to sequential Monte Carlo (SMC) algorithms indexed on the scale parameter. We show how SMC simulation on graphic-processing-units (GPUs) provides very efficient inference for SPA. We also present a scale-mixture representation of the generalized t prior that leads to an EM algorithm to obtain MAP estimates should only these be required.

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