New Directions in Bayesian Model Criticism

贝叶斯模型批评的新方向

• 批准号: 2311108
• 负责人: David Blei
• 金额: $ 22.5万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2026-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2311108&HistoricalAwards=false
• 关键词: New; Directions; Bayesian; Model; Criticism

This project will address the problem of Bayesian model criticism, which is crucial for the effective use of Bayesian statistics and probabilistic machine learning. Currently, the process of designing Bayesian models relies heavily on creativity and experience. This research will develop new statistical tools to evaluate the adequacy of Bayesian models, providing guidance for model design and revision. The project will focus on two innovative approaches: population predictive checks (population PCs) and the posterior predictive null (PPN). These methods combine Bayesian and frequentist ideas to enhance the robustness and rigor of Bayesian model checking. The research will contribute to the foundations of Bayesian statistics, foster connections between different statistical approaches, and advance the field of deep probabilistic models. This will also contribute to the research training of a graduate student who will be involved in the project.Specifically, the research will develop two innovative approaches for Bayesian model criticism that will contribute to the field's technical advancements. The first approach focuses on population predictive checks (population PCs), which combine Bayesian and frequentist principles to provide population-based evaluation of Bayesian models. By leveraging the strengths of both paradigms, this research will develop novel methods that effectively assess the adequacy of Bayesian models, enabling researchers to gain insights into their behavior and performance for informed decisions on model design and revision. The second technical thread centers around the posterior predictive null (PPN), a novel type of model criticism that explores whether data generated from one proposed model can "fool" the model check of another model. By developing statistical tools to address this question, this research will assess the distinctiveness and Bayesian models, and give new directions for finding parsimonious solutions to data modeling. Through theoretical investigations, empirical evaluations, and real-world applications, including medical informatics and computational astrophysics, this research will demonstrate the efficacy of these innovations. The ultimate goal is to provide a comprehensive and practical workflow for building, evaluating, revising, and selecting modern Bayesian models. To ensure widespread access, the algorithms will be disseminated as open-source software, empowering statisticians, scientists, and probabilistic modelers to effectively employ these tools and advance the adoption of Bayesian statistics and probabilistic machine learning methodologies.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目将解决贝叶斯模型批评的问题，这对于有效使用贝叶斯统计和概率机器学习至关重要。当前，设计贝叶斯模型的过程在很大程度上取决于创造力和经验。这项研究将开发新的统计工具来评估贝叶斯模型的充分性，从而为模型设计和修订提供指导。该项目将重点介绍两种创新方法：人群预测检查（人口PC）和后验预测无效（PPN）。这些方法结合了贝叶斯和频繁的思想，以增强贝叶斯模型检查的稳健性和严格性。这项研究将有助于贝叶斯统计的基础，促进不同统计方法之间的联系，并推进深层概率模型的领域。这还将为将参与该项目的研究生的研究培训做出贡献。特别是，该研究将开发两种创新的贝叶斯模型批评方法，这些方法将有助于该领域的技术进步。第一种方法侧重于人群预测检查（人口PC），该检查结合了贝叶斯和频繁的原则，以提供基于人群的贝叶斯模型评估。通过利用这两种范式的优势，这项研究将开发出有效评估贝叶斯模型的充分性的新方法，使研究人员能够深入了解其行为和绩效，以了解模型设计和修订的知情决策。第二个技术线程集中在后验预测零（PPN）周围，这是一种新型的模型批评类型，探讨了从一个建议的模型生成的数据是否可以“愚弄”另一个模型的模型检查。通过开发统计工具来解决这个问题，这项研究将评估独特性和贝叶斯模型，并为寻找数据建模的帕尔西斯解决方案提供了新的方向。通过理论研究，经验评估以及包括医学信息学和计算天体物理学在内的现实应用程序，这项研究将证明这些创新的功效。最终目标是为建造，评估，修改和选择现代贝叶斯模型提供全面而实用的工作流程。为了确保广泛的访问，算法将被传播为开源软件，授权统计学家，科学家和概率建模者有效地采用这些工具并提高采用贝叶斯统计和概率机器学习方法的采用。这项奖项颁发了NSF的法规宣教，并反映了通过评估范围的范围的构成者的构成师的构成师的构成师，并具有宽广的范围。