Conductance bounds on the L 2 convergence rate of Metropolis algorithms on unbounded state spaces
Conductance bounds on the L 2 convergence rate of Metropolis algorithms on unbounded state spaces
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无界状态空间上 Metropolis 算法 L 2 收敛速度的电导界限
DOI：
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发表时间：
2004
影响因子：
1.2
通讯作者：
W. K. Yuen
中科院分区：
文献类型：
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作者：
S. Jarner;W. K. Yuen
在本文中，我们推导出的电导上的界限，从而对大都会算法的频谱间隙上的单调，对数凹的目标密度上的一个区间为100。我们表明，最小的电导集有措施1/2，我们使用这个特性约束的电导方面的算法限制到一个较小的域的电导。而以前的工作电导导致了良好的边界上的马尔可夫链有界域，这是第一个电导界适用于无界域。然后，我们展示了如何将这一结果与Madras和Randall（2002）的状态分解定理相结合，以限制大都会算法的谱间隙，目标分布在α上具有单调的对数凹尾。
In this paper we derive bounds on the conductance and hence on the spectral gap of a Metropolis algorithm with a monotone, log-concave target density on an interval of ℝ. We show that the minimal conductance set has measure ½ and we use this characterization to bound the conductance in terms of the conductance of the algorithm restricted to a smaller domain. Whereas previous work on conductance has resulted in good bounds for Markov chains on bounded domains, this is the first conductance bound applicable to unbounded domains. We then show how this result can be combined with the state-decomposition theorem of Madras and Randall (2002) to bound the spectral gap of Metropolis algorithms with target distributions with monotone, log-concave tails on ℝ.