符合化贝叶斯推断及其在随机划分模型中的应用
Conformalized Bayesian Inference, with Applications to Random Partition Models
AI总结：
该研究提出了一种适用于复杂参数空间的贝叶斯推断方法CBI，通过符合预测原理实现无假设的可信区域和多模态分析，应用于随机划分模型的聚类任务。
摘要：
贝叶斯后验分布自然地代表由数据信息所指导的参数不确定性。然而，当参数空间复杂时，例如在许多非参数设置中，它可能是无限维或组合上很大的时候，标准总结如后验均值、可信区间或简单的多模态概念往往不可用，阻碍了可解释的后验不确定性量化。我们引入了符合化贝叶斯推断（CBI），这是一种广泛适用且计算高效的框架，用于在非标准参数空间上进行后验推断。CBI产生一个点估计，具有无假设的后验覆盖保证的可信区域，以及一个原理性的后验多模态分析，只需从后验中获取马尔可夫链蒙特卡罗样本和参数之间的不一致性概念。该方法为每个参数值构建一个伪密度分数，产生类似于最大似然估计的点估计和由符合预测原理导出的可信区域。这一构造背后的关键概念步骤是将后验推断重新解释为对参数空间的预测。最后的基于密度的聚类步骤识别出代表性的后验模式。我们调查了CBI的多个理论和方法论性质，并展示了其在模拟和真实数据聚类应用中的实用性、可扩展性和多样性，使用随机划分模型。一个配套的Python库cbi_partitions可在github.com/nbariletto/cbi_partitions_repo获得。
英文摘要：
Bayesian posterior distributions naturally represent parameter uncertainty informed by data. However, when the parameter space is complex, as in many nonparametric settings where it is infinite-dimensional or combinatorially large, standard summaries such as posterior means, credible intervals, or simple notions of multimodality are often unavailable, hindering interpretable posterior uncertainty quantification. We introduce Conformalized Bayesian Inference (CBI), a broadly applicable and computationally efficient framework for posterior inference on nonstandard parameter spaces. CBI yields a point estimate, a credible region with assumption-free posterior coverage guarantees, and a principled analysis of posterior multimodality, requiring only Monte Carlo samples from the posterior and a notion of discrepancy between parameters. The method builds a pseudo-density score for each parameter value, yielding a MAP-like point estimate and a credible region derived from conformal prediction principles. The key conceptual step underlying this construction is the reinterpretation of posterior inference as prediction on the parameter space. A final density-based clustering step identifies representative posterior modes. We investigate a number of theoretical and methodological properties of CBI and demonstrate its practicality, scalability, and versatility in simulated and real data clustering applications with random partition models. An accompanying Python library, cbi_partitions, is available at github.com/nbariletto/cbi_partitions_repo.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
