Bayesian model selection, with precedents in George and McCulloch (1993) and Abramovich et al. (1998), support credibility measures that relate model uncertainty, but computation can be costly when sparse priors are approximate. We design an exact selection engine suitable for Gauss noise, t-distributed noise, and logistic learning, benefiting from data-structures derived from coordinate descent lasso. Gibbs sampler chains are stored in a compressed binary format compatible with Equi-Energy (Kou et al., 2006) tempering. We achieve a grouped-effects selection model, similar to the setting for group lasso, to determine co-entry of coefficients into the model. We derive a functional integrand for group inclusion, and introduce a new MCMC switching step to avoid numerical integration. Theorems show this step has exponential convergence to target distribution. We demonstrate a role for group selection to inform on genetic decomposition in a diallel experiment, and identify potential quantitative trait loci in p > 40K Heterogenous Stock haplotype/phenotype studies.

翻译：贝叶斯模型选择（其先例可追溯至George与McCulloch（1993）及Abramovich等（1998））为模型不确定性提供了可信度量支持，但当稀疏先验采用近似形式时，计算成本可能较高。我们设计了一种适用于高斯噪声、t分布噪声及逻辑学习的精确选择引擎，该引擎得益于坐标下降套索（lasso）衍生的数据结构。吉布斯采样器链以压缩二进制格式存储，兼容等能量（Equi-Energy）（Kou等，2006）退火算法。我们构建了一种类似于组套索（group lasso）设置的组效应选择模型，用以确定系数在模型中的共同进入。我们推导了组包含的函数积分形式，并引入一种新的MCMC切换步骤以避免数值积分。定理表明，该步骤以指数速度收敛至目标分布。我们通过双列杂交实验展示了组选择在遗传分解中的信息作用，并在p > 40K的异质品系单倍型/表型研究中识别了潜在的数量性状位点。