Assessing Joint Distributions with Isoprobability Contours

使用等概率轮廓评估联合分布

• 批准号: 0620008
• 负责人: Ali Abbas
• 金额: --
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-01 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0620008&HistoricalAwards=false
• 关键词: Assessing; Joint; Distributions; Isoprobability; Contours

Analogous to the three legs of a stool, the three fundamental bases for any decision are (1) The alternatives, or what we can do; (2) The information, or what we know; and (3) The preferences, or what we like. When faced with uncertainty, people may choose different alternatives based on their taste for risk and the information they have about that uncertain situation. This research focuses on the information element of the decision that is captured by joint probability distributions of several variables. Incorporating dependence is a fundamental step for making inferences about uncertain events or for learning when we receive new information, but eliciting a representative probability distribution is a task that requires care if one is to minimize the effects of cognitive and motivational biases. When eliciting joint probability distributions, we are faced with added difficulties such as conditioning the probability assessments on several variables or assessing dependence parameters between them. These requirements make the assessment of joint probability distributions a difficult task to perform in practice. The objectives of the proposed research are to develop and test a new method for constructing joint probability distributions of continuous random variables using isoprobability contours (contours of points with the same cumulative probability). We explore a new method for constructing isoprobability contours by eliciting pairwise preferences over binary gambles, without the need for numeric responses from the decision maker. This approach facilitates the joint probability assessment significantly. Once the isoprobability contours and at least one one-dimensional marginal probability distribution is determined, is it possible to construct the joint distribution of all the variables present. Thus, we also propose a new method for assessing dependence between the variables of the decision situation using isoprobability contours.

就像凳子的三条腿一样，任何决定的三个基本基础是：(1)选择，或我们能做什么；(2)信息，或我们知道的；(3)偏好，或我们喜欢的。当面临不确定性时，人们可能会根据他们对风险的偏好和他们对不确定情况的了解来选择不同的选择。本研究以多个变量的联合概率分布所捕捉的决策信息元素为研究对象。整合依赖是对不确定事件做出推断或在我们收到新信息时进行学习的基本步骤，但如果要将认知和动机偏见的影响降至最低，得出具有代表性的概率分布是一项需要小心的任务。在推导联合概率分布时，我们面临着额外的困难，例如将概率估计限制在多个变量上，或者估计它们之间的相关性参数。这些要求使得联合概率分布的评估在实践中成为一项困难的任务。这项研究的目的是开发和测试一种利用等概率等值线(具有相同累积概率的点的等值线)来构造连续随机变量的联合概率分布的新方法。我们探索了一种构造等概率等值线的新方法，该方法通过诱导两两的偏好而不是二元赌博，而不需要决策者的数字响应。这种方法极大地方便了联合概率评估。一旦确定了等概率等值线和至少一个一维边缘概率分布，就可以构造存在的所有变量的联合分布。因此，我们还提出了一种利用等概率等值线来评估决策情况变量之间相关性的新方法。