Collaborative Research: Bayesian Approaches For Testing Axioms of Measurement

许多衡量和决策模型都可以用公理来描述。虽然检验数据是否符合这样的公理是最重要的，但经验数据和公理的性质之间存在着挑战性的不相容。一方面，经验数据通常包含随机误差，这可归因于许多来源，如人类(或动物)行为的固有不可靠性、抽样误差和观测本身的不精确。另一方面，公理不考虑随机误差，因为它们是确定性的、定性的形式。本研究项目旨在通过开发基于现代贝叶斯模型估计、模型拟合评估和模型选择方法的公理检验程序来解决这种不相容问题。通过五个相互关联的研究目标，本项目将通过应用贝叶斯推理框架在真实数据上测试公理，并通过比较不同类型的模型选择方法和先验分布的性能来研究贝叶斯推理框架。这项工作的目的是确定测试测量公理的最佳贝叶斯推理方法。对于包括测试理论和决策理论在内的许多社会科学分支的研究人员来说，这项工作的成果应该为测试当代测量和决策模型所依据的关键假设提供可用和强大的统计工具。这些统计工具的使用应有助于更好地理解这些模型，并可能表明它们是有成效的扩展。

Many models of measurement and decision-making can be characterized in terms of axioms. While it is of primary importance to test whether data are in accord to such axioms, there is a challenging incompatibility between empirical data and the nature of the axioms. On the one hand, empirical data generally contain random error, which is attributable to a number of sources, such as the inherent unreliability of human (or animal) behavior, sampling error, and imprecision of the observations themselves. On the other hand, the axioms do not account for random error, because of their deterministic, qualitative form. This research project aims to solve this incompatibility by developing procedures of axiom testing that are based on contemporary Bayesian methods of model estimation, model fit evaluation, and model selection. Through five inter-related research objectives, this project will investigate the Bayes inference framework by applying it to test axioms on real data, and by comparing the performance of different types of model selection methods and prior distributions. The goal is to determine the best Bayesian inference methods for testing axioms of measurement.For researchers in many branches of the social sciences, including test theory and decision theory, the fruits of this work should provide usable and powerful statistical tools for testing the key assumptions that underlies contemporary models of measurement and decision-making. The use of these statistical tools should lead to a better understanding of these models, and possibly indicate productive extensions of them.