HAAR-WEAVE-METROPOLIS KERNEL
HAAR-WEAVE-METROPOLIS KERNEL
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DOI：
10.5109/4755997
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发表时间：
2021-11
期刊：
影响因子：
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通讯作者：
K. Kamatani;Xiaolin Song
中科院分区：
文献类型：
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作者：
K. Kamatani;Xiaolin Song
最近，受哈密顿蒙特卡罗方法的启发，许多马尔可夫链蒙特卡罗方法被开发出来，并具有确定性可逆变换建议。确定性变换相对容易与目标分布的局部信息（梯度等）相协调。然而，正如遍历理论所表明的那样，这些确定性提议方法似乎与鲁棒性不相容并导致收敛性差，特别是在目标分布具有重尾的情况下。另一方面，使用 Haar 度量的马尔可夫核相对稳健，因为它通过引入全局参数来学习有关目标分布的全局信息。然而，它需要密度保持条件，并且许多确定性建议打破了这个条件。在本文中，我们仔细选择了保留结构的确定性变换，并使用确定性变换创建了马尔可夫核（Weave-Metropolis 核）。通过与 Haar 度量相结合，我们还引入了 Haar-Weave-Metropolis 内核。这样，马尔可夫核可以利用确定性提案来利用目标分布的局部信息，并且由于哈尔测度，它可以利用目标分布的全局信息。最后，我们通过数值实验表明，该方法在有效样本量和每秒均方跳跃距离方面的性能优于其他方法。
Recently, many Markov chain Monte Carlo methods have been developed with deterministic reversible transform proposals inspired by the Hamiltonian Monte Carlo method. The deterministic transform is relatively easy to reconcile with the local information (gradient etc.) of the target distribution. However, as the ergodic theory suggests, these deterministic proposal methods seem to be incompatible with robustness and lead to poor convergence, especially in the case of target distributions with heavy tails. On the other hand, the Markov kernel using the Haar measure is relatively robust since it learns global information about the target distribution introducing global parameters. However, it requires a density preserving condition, and many deterministic proposals break this condition. In this paper, we carefully select deterministic transforms that preserve the structure and create a Markov kernel, the Weave-Metropolis kernel, using the deterministic transforms. By combining with the Haar measure, we also introduce the Haar-Weave-Metropolis kernel. In this way, the Markov kernel can employ the local information of the target distribution using the deterministic proposal, and thanks to the Haar measure, it can employ the global information of the target distribution. Finally, we show through numerical experiments that the performance of the proposed method is superior to other methods in terms of effective sample size and mean square jump distance per second.