贝叶斯评分校准的灵活变换
Flexible Transformations for Bayesian Score Calibration
- Queensland University of Technology（昆士兰科技大学）
- Adelaide University（阿德莱德大学）
- National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出两种灵活变换（多项式扩展和顺序应用）用于贝叶斯评分校准，以修正复杂模型误差，并在模拟研究中展示其优于现有方法。
AI中文摘要：
现代统计模型为了真实地捕捉系统动态而变得越来越复杂。使用标准的基于模拟的推断，这些模型可能在计算上难以承受，因此需要使用模型校准方法。贝叶斯评分校准是一种计算高效的模型校准框架，具有强大的理论保证。该框架利用少量来自数据生成过程的模拟，为近似模型学习适当的修正。目前，仅探索了位置-尺度变换，这可能缺乏灵活性来修正某些近似模型引入的复杂误差。在本文中，我们为贝叶斯评分校准框架开发了两种灵活变换。第一种是多项式扩展，可以适当地调整具有位置变化误差的近似模型。第二种是贝叶斯评分校准的顺序应用，可以适应其后验对真实参数值支持度较低的近似模型。我们还讨论了与该框架一起使用的额外诊断方法。我们在两项说明性模拟研究中证明了这两种方法相对于贝叶斯评分校准所提供的增强灵活性。
英文摘要：
Modern statistical models are growing increasingly complex in an effort to realistically capture system dynamics. Using standard simulation-based inference, these models may be computationally prohibitive, necessitating the use of model calibration methods. Bayesian score calibration is a computationally efficient framework for model calibration with strong theoretical guarantees. This framework learns an appropriate correction for an approximate model using a small number of simulations from the data-generating process. Currently, only a location-scale transformation has been explored, which may lack the flexibility to correct the complex error introduced by some approximate models. In this paper, we develop two flexible transformations for use in the Bayesian score calibration framework. The first is a polynomial extension, which can appropriately adjust approximate models with location-varying error. The second is a sequential application of Bayesian score calibration, which can accommodate approximate models with posteriors that have low support for the true parameter values. We also discuss an additional diagnostic for use with this framework. We demonstrate the increased flexibility these two approaches provide over Bayesian score calibration in two illustrative simulation studies.
