遍历性
遍历理论
统计物理学
哈密顿量(控制论)
蒙特卡罗方法
职位(财务)
数学
马尔科夫蒙特卡洛
马尔可夫链
混合蒙特卡罗
参数空间
作者
Samuel Livingstone,Michael Betancourt,Simon Byrne,Mark Girolami
出处
期刊:arXiv: Computation
日期:2016-01-29
被引量:16
摘要
We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations with both position-independent and position-dependent integration times. In the former case we find that the conditions for geometric ergodicity are essentially a gradient of the log-density which asymptotically points towards the centre of the space and grows no faster than linearly. In an idealised scenario in which the integration time is allowed to change in different regions of the space, we show that geometric ergodicity can be recovered for a much broader class of tail behaviours, leading to some guidelines for the choice of this free parameter in practice.
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