Foundations of Bayesian Theory: Extensions and Applications

贝叶斯理论的基础：扩展和应用

• 批准号: 0314249
• 负责人: Edi Karni
• 金额: $ 17.79万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-11-01 至 2007-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0314249&HistoricalAwards=false
• 关键词: Foundations; Bayesian; Theory; Extensions; Applications

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.

自 20 世纪初以来，社会科学家对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之外，这项调查还旨在提供贝叶斯统计和主观预期效用理论的行为基础，该理论通常用于对经济学不确定性下的决策进行建模。现有理论未能实现上述目标，这促使我在贝叶斯理论的基础上开发了一种新方法，该方法在我的工作中进行了描述。该项目的目标是扩大范围并检查这种方法的一些应用。该研究涉及数学分析在两个层面上的应用：对于设想的扩展，该方法是公理化的，预期结果是表示定理，即分别通过效用函数和概率度量来表达个人偏好和信念。应用涉及带有道德风险的失业保险数学模型及其分析。目的是将现有的最佳失业保险结果与新理论下的最佳失业保险计划进行比较，并认识到这些结果可能基于可能无法代表失业者对其求职活动可能成功的信念的概率。该项目还将解决表达个人信念的概率的问题。这项研究将强调正确评估个人信念的理论和实证重要性，以设计激励契约和公共政策，其中激励问题至关重要。它还将扩展统计分析中使用的贝叶斯方法的行为基础。