Bayes Factor Methods for Model Comparison in the Social Sciences

社会科学中模型比较的贝叶斯因子方法

• 批准号: 1260806
• 负责人: Dongchu Sun
• 金额: $ 15万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-04-01 至 2015-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1260806&HistoricalAwards=false
• 关键词: Bayes; Factor; Methods; Model; Comparison

The project will develop Bayes factors for common research designs. Bayes factors provide an attractive alternative to conventional significance tests, in particular to F-tests for linear models. They have failed, however, to achieve broad acceptance for at least two reasons: They are perceived as having an undesirable dependence on the chosen prior distribution, and they are viewed as being difficult to compute. To address the first concern, Bayes factors for a class of "default" priors will be developed; this is, with priors that result in Bayes factors with desirable theoretical properties, impart a minimal degree of information, and are broadly applicable in a wide range of common designs. One natural property of a desirable prior is "consistency," the ability to support the correct model in the large sample limit. The focus is on consistency when the model dimension is relatively large compared to the sample size, as is common in many ANOVA designs. Consistency will be proved for common one-way and two-way and possibly higher order designs. With respect to the second concern, computation entails integration across perhaps many dimensions. There are several choices (including quadrature, Monte Carlo sampling, bridge sampling, Laplace approximation, or Savage-Dickey density ratio estimation), and which choice works best will vary depending on the sample size and design. Heuristics for picking a method of computation that is quick and efficient will be developed. The end result will be the development of easy-to-compute Bayes factors with excellent properties.The physical sciences have made gains by identifying invariances -- those elements that stay constant when others change. In contrast, the social sciences have emphasized demonstrations of effects rather than of invariances. One difficulty in demonstrating invariances in noisy environments is methodological -- conventional hypothesis testing allows researchers to amass evidence against the null but never for it. Bayes factors provide an ideal solution because they can be used to assess evidence for the null or alternative, are straightforward to interpret, and provide a natural penalty for model complexity. The project's ultimate goal is that Bayes factors become a widely-adopted, everyday method in substantive researchers' methodological toolkit. To that end, the project will develop a series of software applications. Some of these will be R packages for methodologists. Others will be web applets and GUI software for substantive researchers without statistical expertise. These latter products will be very easy to use, and this ease should encourage rapid adoption. In addition, conference workshops and tutorials, including short courses, are planned in the investigators' respective disciplines.

该项目将为共同的研究设计开发贝叶斯因子。 贝叶斯因子为传统的显著性检验提供了一种有吸引力的替代方法，特别是线性模型的F检验。 然而，它们未能获得广泛接受，至少有两个原因：它们被认为对所选择的先验分布有不期望的依赖性，并且它们被认为难以计算。 为了解决第一个问题，贝叶斯因子的一类“默认”先验将开发，这是先验，导致贝叶斯因子与理想的理论属性，赋予最小程度的信息，并广泛适用于各种常见的设计。 理想先验的一个自然属性是“一致性”，即在大样本限制下支持正确模型的能力。 当模型维度与样本量相比相对较大时，重点是一致性，这在许多ANOVA设计中很常见。 将证明常见的单向和双向以及可能的高阶设计的一致性。 关于第二个问题，计算需要跨越许多维度的整合。 有几种选择（包括求积、蒙特卡罗采样、桥式采样、拉普拉斯近似或萨维奇-迪基密度比估计），哪种选择效果最好将取决于样本量和设计。 将开发用于挑选快速有效的计算方法的启发式。 最终的结果将是开发出易于计算的具有优良特性的贝叶斯因子。物理科学通过识别不变量--当其他元素发生变化时保持不变的元素--而取得了进展。 相反，社会科学强调的是效果的证明，而不是不变性。 在嘈杂的环境中证明不变性的一个困难是方法-传统的假设检验允许研究人员收集反对零的证据，但从来没有为它。贝叶斯因子提供了一个理想的解决方案，因为它们可以用来评估零或替代的证据，是简单的解释，并提供了一个自然的惩罚模型的复杂性。 该项目的最终目标是使贝叶斯因子成为大量研究人员方法工具包中广泛采用的日常方法。 为此，该项目将开发一系列应用软件。 其中一些将是方法学家的R包。 其他软件将是供没有统计专门知识的实务研究人员使用的网络小程序和图形用户界面软件。 后一种产品将非常易于使用，这种易用性将鼓励快速采用。 此外，还计划在调查员各自的学科举办会议讲习班和辅导班，包括短期课程。