Conditions for Rapid and Torpid Mixing of Parallel and Simulated Tempering on Multimodal Distributions
Conditions for Rapid and Torpid Mixing of Parallel and Simulated Tempering on Multimodal Distributions
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多峰分布上平行模拟回火快速缓慢混合的条件
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
M. Huber
中科院分区：
文献类型：
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作者：
D. Woodard;S. Schmidler;M. Huber
我们获得了通过并行和模拟回火构造的马尔可夫链收敛率的上限。这些界限用于为两种技术的缓慢混合提供一组充分的条件。我们应用这些条件来显示三个示例的平行回火和模拟回火的迟钝混合：R M 中具有不等协方差的正态混合模型和 q 3 的平均场 Potts 模型，无论温度的数量和选择如何，以及选择不充分的温度集时的平均场伊辛模型。后一个结果与如前所示的线性增加温度组的平均伊辛模型上的平行回火和模拟回火的快速混合形成对比。
We obtain upper bounds on the convergence rates of Markov chains constructed by parallel and simulated tempering. These bounds are used to provide a set of sucien t conditions for torpid mixing of both techniques. We apply these conditions to show torpid mixing of parallel and simulated tempering for three examples: a normal mixture model with unequal covariances in R M and the mean-eld Potts model with q 3, regardless of the number and choice of temperatures, and the meaneld Ising model when an insucien t set of temperatures is chosen. The latter result contrasts with the rapid mixing of parallel and simulated tempering on the meaneld Ising model with a linearly increasing set of temperatures as shown previously.