标题： 逃离Neal的漏斗：分阶段抽样方法用于分层模型 显示英文标题

标题： Escaping Neal's Funnel: a multi-stage sampling method for hierarchical models

摘要： Neal's funnel 指的是在贝叶斯分层模型中常见的概率密度指数衰减现象。 通常的采样方法，如马尔可夫链蒙特卡洛，难以高效地对 funnel 进行采样。 重新参数化模型或对局部参数进行解析边缘化是修复表现出 Neal's funnel 的分布中的采样病理的常用技术。 在本文中，我们表明通过进行分层分析，可以避免 Neal's funnel 的挑战，即，以分层的方式进行。 也就是说，而不是联合采样分层模型的所有参数，我们将采样分为多个阶段。 第一阶段采样一个广义的（高维的）分层模型，该模型被参数化以减轻 funnel 的陡峭程度。 下一阶段从第一阶段估计的密度中进行采样，但受到一个约束，该约束限制采样以恢复原始（低维的）分层模型超参数的边缘分布。 可以使用归一化流来表示第一阶段的分布，以便于在分析的第二阶段轻松进行采样。 当有效的重新参数化计算成本较高，或者已经存在一个容易采样的广义分层模型时，这种技术是有用的。 显示英文摘要

摘要： Neal's funnel refers to an exponential tapering in probability densities common to Bayesian hierarchical models. Usual sampling methods, such as Markov Chain Monte Carlo, struggle to efficiently sample the funnel. Reparameterizing the model or analytically marginalizing local parameters are common techniques to remedy sampling pathologies in distributions exhibiting Neal's funnel. In this paper, we show that the challenges of Neal's funnel can be avoided by performing the hierarchical analysis, well, hierarchically. That is, instead of sampling all parameters of the hierarchical model jointly, we break the sampling into multiple stages. The first stage samples a generalized (higher-dimensional) hierarchical model which is parameterized to lessen the sharpness of the funnel. The next stage samples from the estimated density of the first stage, but under a constraint which restricts the sampling to recover the marginal distributions on the hyper-parameters of the original (lower-dimensional) hierarchical model. A normalizing flow can be used to represent the distribution from the first stage, such that it can easily be sampled from for the second stage of the analysis. This technique is useful when effective reparameterizations are computationally expensive to calculate, or a generalized hierarchical model already exists from which it is easy to sample.