Discontinuous Hamiltonian Monte Carlo for models with discrete parameters and discontinuous likelihoods
Discontinuous Hamiltonian Monte Carlo for models with discrete parameters and discontinuous likelihoods
复制标题
适用于具有离散参数和不连续似然的模型的不连续哈密顿蒙特卡罗
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Jianfeng Lu
中科院分区：
文献类型：
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作者：
A. Nishimura;D. Dunson;Jianfeng Lu
哈密顿蒙特卡罗已成为后验计算的标准工具。在本文中，我们提出了一个扩展，可以有效地探索具有不连续密度的目标分布。我们的扩展尤其能够通过将概率质量函数嵌入到连续空间中来从序数参数中进行有效采样。我们通过不连续哈密顿动力学理论来激发我们的方法，并开发了相应的数值求解器。所提出的求解器是同类中的第一个，具有精确保留哈密顿量的卓越能力。我们将我们的算法应用于具有挑战性的后验推理问题，以证明其广泛的适用性和竞争性能。
Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article, we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables efficient sampling from ordinal parameters though embedding of probability mass functions into continuous spaces. We motivate our approach through a theory of discontinuous Hamiltonian dynamics and develop a corresponding numerical solver. The proposed solver is the first of its kind, with a remarkable ability to exactly preserve the Hamiltonian. We apply our algorithm to challenging posterior inference problems to demonstrate its wide applicability and competitive performance.