For Bayesian learning, given likelihood function and Gaussian prior, the elliptical slice sampler, introduced by Murray, Adams and MacKay 2010, provides a tool for the construction of a Markov chain for approximate sampling of the underlying posterior distribution. Besides of its wide applicability and simplicity its main feature is that no tuning is necessary. Under weak regularity assumptions on the posterior density we show that the corresponding Markov chain is geometrically ergodic and therefore yield qualitative convergence guarantees. We illustrate our result for Gaussian posteriors as they appear in Gaussian process regression, as well as in a setting of a multi-modal distribution. Remarkably, our numerical experiments indicate a dimension-independent performance of elliptical slice sampling even in situations where our ergodicity result does not apply.
翻译:对于Bayesian的学习,考虑到可能性功能和Gaussian之前的情况,由Murray、Adams和MacKay于2010年推出的椭圆切片采样器提供了一种工具,用于建造Markov链条,以大致取样基础的后表分布,除了其广泛适用性和简单性之外,其主要特征是不需要调整。在对后表密度的常规性假设薄弱的情况下,我们表明相应的Markov链条具有几何异性,因此产生质趋同保证。我们用高斯进程回归和多模式分布的设置来说明高斯后表的后表,以及多模式分布的设置。值得注意的是,我们的数字实验表明,即使在我们的切片结果不适用的情况下,其采样的尺寸也是独立的。