Foundations of Bayesian Theory: Extensions and Applications

自世纪初以来，社会科学家们就对用概率来量化个人对各种事件可能实现的信念的可能性感兴趣。除了明显的哲学兴趣，这项研究旨在提供贝叶斯统计和主观预期效用理论的行为基础，该理论通常用于经济学中不确定性下的决策模型。现有理论未能达到上述目标，促使我在贝叶斯理论的基础上开发了一种新方法。本项目的目标是扩大范围，并审查这种方法的一些应用。该研究涉及应用数学分析在两个层面上：对于设想的扩展的方法是公理和预期的结果是表示定理，即个人的偏好和信念的表达，分别由效用函数和概率措施。应用包括失业保险的数学建模和道德风险分析。我们的目标是比较现有的最优失业保险的结果，认识到这些结果可能是基于概率，可能不代表他们的求职活动的可能成功的失业信念，最优失业保险计划下的新理论。本课题还将探讨表达个人信念的概率的引出问题，并强调正确评估个人信念对于设计激励性合同和激励性问题必不可少的公共政策的理论和实证重要性。它还将扩展统计分析中使用的贝叶斯方法的行为基础。

Since the beginning of the 20th century social scientists were interested in the possibility of quantifying individual beliefs about the likely realization of various events with probabilities. In addition to the obvious philosophical interest this inquiry was intended to provide a behavioral foundations of Bayesian statistics and of subjective expected utility theory that is often used to model decision-making under uncertainty in economics. The failure of exiting theories to attain the aforementioned goal motivated the development of a new approach described in my work on the foundations of Bayesian theory. The objective of this project is to extend the scope and to examine some applications of this approach. The research involves the application of mathematical analysis at two levels: For the envisioned extensions the method is axiomatic and the expected results are representation theorems, namely, the expression of individual preferences and beliefs, respectively, by utility functions and probability measures. The applications involve mathematical modeling of unemployment insurance with moral hazard and its analysis. The objective is to compare the exiting results on optimal unemployment insurance, recognizing that these results may be based on probabilities that may not represent the unemployed beliefs about the likely success of their job-search activities, to the optimal unemployment insurance program under the new theory. The project will also address the issue of elicitation of probabilities that express individual beliefs.This research will highlight the theoretical and empirical importance of correctly assessing individual beliefs for the purpose of designing incentive contracts and public policies in which incentive issues are essential. It will also extend the behavioral basis of the Bayesian methods used in statistical analysis.