We extend elliptical slice sampling, a Markov chain transition kernel suggested in Murray, Adams and MacKay 2010, to infinite-dimensional separable Hilbert spaces and discuss its well-definedness. We point to a regularity requirement, provide an alternative proof of the desirable reversibility property and show that it induces a positive semi-definite Markov operator. Crucial within the proof of the formerly mentioned results is the analysis of a shrinkage Markov chain that may be interesting on its own.

翻译：我们将椭圆切片采样（Murray, Adams and MacKay 2010提出的马尔可夫链转移核）扩展到无限维可分希尔伯特空间，并讨论其良定性。我们指出一个正则性要求，给出该理想可逆性质的替代证明，并证明其诱导出一个正半定马尔可夫算子。在先前所述结果的证明中，一个可能独立成趣的收缩马尔可夫链分析起到了关键作用。