论文标题
亚稳态后分布中的自适应路径采样
Adaptive Path Sampling in Metastable Posterior Distributions
论文作者
论文摘要
标准化常数在贝叶斯计算中起着重要作用，并且关于计算或近似归一化常数的方法，无法以封闭形式进行评估。当归一化常数因数量级而变化时，基于重要性采样的方法可能需要进行多轮调整。我们使用自适应路径采样提出了一种改进的方法，从而迭代地减少了基座和目标之间的差距。使用这种自适应策略，我们开发了两个亚稳态抽样方案。它们是在Stan中自动化的，几乎不需要调整。对于多模式后密度，我们为模拟的回火配备连续温度。对于漏斗形的熵屏障，我们会自适应地增加瓶颈区域的质量，形成一个隐式分裂和矛盾。两种方法在经验上的表现都比现有的方法更好，用于从亚稳态分布中取样，包括更高的准确性和计算效率。
The normalizing constant plays an important role in Bayesian computation, and there is a large literature on methods for computing or approximating normalizing constants that cannot be evaluated in closed form. When the normalizing constant varies by orders of magnitude, methods based on importance sampling can require many rounds of tuning. We present an improved approach using adaptive path sampling, iteratively reducing gaps between the base and target. Using this adaptive strategy, we develop two metastable sampling schemes. They are automated in Stan and require little tuning. For a multimodal posterior density, we equip simulated tempering with a continuous temperature. For a funnel-shaped entropic barrier, we adaptively increase mass in bottleneck regions to form an implicit divide-and-conquer. Both approaches empirically perform better than existing methods for sampling from metastable distributions, including higher accuracy and computation efficiency.
