The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain Monte Carlo methods do not perform well in typical problem sizes of interest. The current paper proposes new adaptive Markov chain Monte Carlo algorithms to address this shortcoming. The adaptive design of these algorithms exploits the observation that in large $p$ small $n$ settings, the majority of the $p$ variables will be approximately uncorrelated a posteriori. The algorithms adaptively build suitable non-local proposals that result in moves with squared jumping distance significantly larger than standard methods. Their performance is studied empirically in high-dimensional problems (with both simulated and actual data) and speedups of up to 4 orders of magnitude are observed. The proposed algorithms are easily implementable on multi-core architectures and are well suited for parallel tempering or sequential Monte Carlo implementations.

中文翻译：

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寻找丢失的混合时间：具有非常大 p 的贝叶斯变量选择的自适应马尔可夫链蒙特卡罗方案

具有大量变量的数据集的可用性正在迅速增加。贝叶斯变量选择方法对这些数据集的回归的有效应用已被证明是困难的，因为可用的马尔可夫链蒙特卡罗方法在典型的感兴趣的问题规模上表现不佳。目前的论文提出了新的自适应马尔可夫链蒙特卡罗算法来解决这个缺点。这些算法的自适应设计利用了以下观察结果：在大 $p$ 小 $n$ 设置中，大多数 $p$ 变量将是近似不相关的后验。算法自适应地构建合适的非局部提议，导致平方跳跃距离明显大于标准方法的移动。在高维问题（具有模拟和实际数据）中对它们的性能进行了实证研究，并观察到高达 4 个数量级的加速。所提出的算法很容易在多核架构上实现，并且非常适合并行调温或顺序蒙特卡罗实现。