The regional adaptive (RAPT) algorithm is particularly useful in sampling from multimodal distributions. We propose an adaptive partitioning of the sample space, to be used in conjunction with the RAPT sampler and its variants. The adaptive partitioning consists in defining a hyperplane that is orthogonal to the line joining averaged coordinates in two separate regions and that goes through a point such that both averaged coordinates are equally Mahalanobis-distant from this point. This yields an adaptive process that is robust to the choice of initial partition, stabilizes rapidly and is implemented at a marginal computational cost. The ergodicity of the sampler is verified through the simultaneous uniform ergodicity and diminishing adaptation conditions. The approach is compared to the RAPT algorithm with fixed regions and to the RAPT with online recursion (RAPTOR) through various examples, including a real data application. In short, our main contribution is the development of an alternative version of RAPTOR that seems to have no obvious downside and runs 15–35% faster in the examples considered.

中文翻译：

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区域自适应算法中样本空间的在线划分

区域自适应 (RAPT) 算法在从多峰分布中采样时特别有用。我们提出了样本空间的自适应分区，与 RAPT 采样器及其变体结合使用。自适应分区包括定义一个超平面，该超平面与连接两个单独区域中的平均坐标的线正交，并且该超平面经过一个点，使得两个平均坐标距该点的马氏距离相等。这产生了一个自适应过程，该过程对初始分区的选择具有鲁棒性，快速稳定并以边际计算成本实现。采样器的遍历性通过同时的均匀遍历性和递减适应来验证 使适应。通过包括真实数据应用在内的各种示例，将该方法与具有固定区域的 RAPT 算法和具有在线递归 (RAPTOR) 的 RAPT 算法进行了比较。简而言之，我们的主要贡献是开发了 RAPTOR 的替代版本，它似乎没有明显的缺点，并且在所考虑的示例中运行速度提高了 15-35%。