New Directions in Bayesian Model Criticism

该项目将解决贝叶斯模型批评问题，这对于有效使用贝叶斯统计和概率机器学习至关重要。目前，设计贝叶斯模型的过程很大程度上依赖于创造力和经验。本研究将开发新的统计工具来评估贝叶斯模型的充分性，为模型设计和修正提供指导。该项目将侧重于两种创新方法：人口预测检查（population pc）和后验预测零值（PPN）。这些方法结合了贝叶斯和频率思想，增强了贝叶斯模型检验的鲁棒性和严谨性。该研究将有助于奠定贝叶斯统计的基础，促进不同统计方法之间的联系，并推动深度概率模型领域的发展。这也将有助于将参与该项目的研究生的研究训练。具体来说，该研究将为贝叶斯模型批评开发两种创新方法，这将有助于该领域的技术进步。第一种方法侧重于种群预测检查（population pc），它将贝叶斯和频率原理结合起来，提供基于种群的贝叶斯模型评估。通过利用这两种范式的优势，本研究将开发出有效评估贝叶斯模型充足性的新方法，使研究人员能够深入了解贝叶斯模型的行为和性能，从而在模型设计和修订方面做出明智的决策。第二条技术线索围绕后验预测零值（PPN）展开，这是一种新型的模型批评，探讨从一个提出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，本研究将评估贝叶斯模型的独特性，并为寻找数据建模的简约解决方案提供新的方向。通过理论调查、实证评估和现实世界的应用，包括医学信息学和计算天体物理学，本研究将证明这些创新的有效性。最终目标是为构建、评估、修改和选择现代贝叶斯模型提供一个全面而实用的工作流程。为了确保广泛的访问，这些算法将作为开源软件传播，使统计学家、科学家和概率建模者能够有效地使用这些工具，并推进贝叶斯统计和概率机器学习方法的采用。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.