In Bayesian statistics, exploring high-dimensional multimodal posterior distributions poses major challenges for existing MCMC approaches. This paper introduces the Annealed Leap-Point Sampler (ALPS), which augments the target distribution state space with modified annealed (cooled) distributions, in contrast to traditional tempering approaches. The coldest state is chosen such that its annealed density is well-approximated locally by a Laplace approximation. This allows for automated setup of a scalable mode-leaping independence sampler. ALPS requires an exploration component to search for the mode locations, which can either be run adaptively in parallel to improve these mode-jumping proposals, or else as a pre-computation step. A theoretical analysis shows that for a d-dimensional problem the coolest temperature level required only needs to be linear in dimension, $\mathcal{O}\left(d\right)$, implying that the number of iterations needed for ALPS to converge is $\mathcal{O}\left(d\right)$ (typically leading to overall complexity $\mathcal{O}\left(d^3\right)$ when computational cost per iteration is taken into account). ALPS is illustrated on several complex, multimodal distributions that arise from real-world applications. This includes a seemingly-unrelated regression (SUR) model of longitudinal data from U.S. manufacturing firms, as well as a spectral density model that is used in analytical chemistry for identification of molecular biomarkers.

翻译：在贝叶斯统计中，探索高维多峰后验分布对现有MCMC方法构成重大挑战。本文提出退火跃迁点采样器（ALPS），该方法通过改进的退火（冷却）分布扩展目标分布状态空间，与传统回火方法形成对比。最冷状态的选取使得其退火密度可通过拉普拉斯近似在局部获得良好逼近。这为建立可扩展的模态跃迁独立采样器提供了自动化设置方案。ALPS需要探索组件来搜索模态位置，该组件既可作为预计算步骤运行，也可并行自适应执行以优化模态跳跃提议。理论分析表明，对于d维问题，所需的最低温度层级仅需与维度呈线性关系$\mathcal{O}\left(d\right)$，这意味着ALPS收敛所需迭代次数为$\mathcal{O}\left(d\right)$（考虑每次迭代计算成本时通常导致总体复杂度为$\mathcal{O}\left(d^3\right)$）。ALPS在多个源自实际应用的复杂多峰分布上得到验证，包括对美国制造业企业纵向数据建立的看似无关回归（SUR）模型，以及分析化学中用于分子生物标志物识别的谱密度模型。