论文标题
强大的随机步行状大都市悬挂算法，用于集中后代
Robust random walk-like Metropolis-Hastings algorithms for concentrating posteriors
论文作者
论文摘要
通过贝叶斯推断，我们通过高度信息数据进行了分析，我们分析了随机步行样的大都市悬挂算法的性能，以近似越来越集中的目标分布采样。我们专注于使用基于黑森的目标协方差近似的高斯建议。通过推动的过渡内核，我们表明，对于高斯目标，相应的大都市悬挂算法的光谱间隙独立于后方的浓度，即用于贝叶斯推理的观测数据中的噪声水平。此外，通过利用浓缩后期的收敛性，我们将分析扩展到非高斯目标度量，该目标要么集中在单个点或沿线性歧管围绕。特别是，在这种情况下，我们表明，随着目标浓缩量，合适的大都会悬挂的平均接收率和预期的平方距离马尔可夫链的跳跃距离不会恶化。
Motivated by Bayesian inference with highly informative data we analyze the performance of random walk-like Metropolis-Hastings algorithms for approximate sampling of increasingly concentrating target distributions. We focus on Gaussian proposals which use a Hessian-based approximation of the target covariance. By means of pushforward transition kernels we show that for Gaussian target measures the spectral gap of the corresponding Metropolis-Hastings algorithm is independent of the concentration of the posterior, i.e., the noise level in the observational data that is used for Bayesian inference. Moreover, by exploiting the convergence of the concentrating posteriors to their Laplace approximation we extend the analysis to non-Gaussian target measures which either concentrate around a single point or along a linear manifold. In particular, in that setting we show that the average acceptance rate as well as the expected squared jump distance of suitable Metropolis-Hastings Markov chains do not deteriorate as the target concentrates.
