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首页> 外文期刊>Journal of computational and graphical statistics: A joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America >An Adaptive Parallel Tempering Algorithm
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An Adaptive Parallel Tempering Algorithm

机译：自适应并行回火算法

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摘要

Parallel tempering is a generic Markov chainMonteCarlo samplingmethod which allows good mixing with multimodal target distributions, where conventionalMetropolis-Hastings algorithms often fail. The mixing properties of the sampler depend strongly on the choice of tuning parameters, such as the temperature schedule and the proposal distribution used for local exploration. We propose an adaptive algorithm with fixed number of temperatures which tunes both the temperature schedule and the parameters of the random-walk Metropolis kernel automatically. We prove the convergence of the adaptation and a strong law of large numbers for the algorithm under general conditions. We also prove as a side result the geometric ergodicity of the parallel tempering algorithm. We illustrate the performance of our method with examples. Our empirical findings indicate that the algorithm can cope well with different kinds of scenarios without prior tuning. Supplementary materials including the proofs and the Matlab implementation are available online.
机译：平行回火是通用的马尔可夫链蒙特卡洛采样方法，它可以与多峰目标分布良好地混合，而传统的Metropolis-Hastings算法通常会失败。采样器的混合属性在很大程度上取决于调整参数的选择，例如温度计划和用于局部勘探的建议分布。我们提出了一种具有固定温度数的自适应算法，该算法可自动调整温度调度和随机游动Metropolis内核的参数。我们证明了在一般条件下算法的自适应收敛性和强大的大量定律。作为辅助结果，我们还证明了平行回火算法的几何遍历性。我们通过示例来说明我们方法的性能。我们的经验发现表明，该算法无需事先调整即可很好地应对各种情况。包括证明和Matlab实现的补充材料可在线获得。

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