Constantine et al. (2016) introduced a Metropolis-Hastings (MH) approach that target the active subspace of a posterior distribution: a linearly projected subspace that is informed by the likelihood. Schuster et al. (2017) refined this approach to introduce a pseudo-marginal Metropolis-Hastings, integrating out inactive variables through estimating a marginal likelihood at every MH iteration. In this paper we show empirically that the effectiveness of these approaches is limited in the case where the linearity assumption is violated, and suggest a particle marginal Metropolis-Hastings algorithm as an alternative for this situation. Finally, the high computational cost of these approaches leads us to consider alternative approaches to using active subspaces in MCMC that avoid the need to estimate a marginal likelihood: we introduce Metropolis-within-Gibbs and Metropolis-within-particle Gibbs methods that provide a more computationally efficient use of the active subspace.

翻译：Constantine 等人 (2016) 提出了一种针对后验分布活动子空间的 Metropolis-Hastings (MH) 方法：该线性投影子空间由似然函数所决定。Schuster 等人 (2017) 改进了该方法，提出了一种伪边际 Metropolis-Hastings 方法，通过在每次 MH 迭代中估计边际似然来积分掉非活动变量。本文通过实证表明，在线性假设不成立的情况下，这些方法的有效性有限，并建议在这种情况下采用粒子边际 Metropolis-Hastings 算法作为替代方案。最后，这些方法的高计算成本促使我们考虑在 MCMC 中使用活动子空间的替代方案，以避免估计边际似然的需要：我们引入了 Metropolis-within-Gibbs 和 Metropolis-within-particle Gibbs 方法，它们为活动子空间的使用提供了更高的计算效率。