Assessing Joint Distributions with Isoprobability Contours

类似于凳子的三条腿，任何决定的三个基本基础是：(1)选择，或者我们能做什么；(2)信息，或我们所知道的；(3)偏好，或者说我们喜欢什么。当面对不确定性时，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。本研究的重点是由多个变量的联合概率分布所捕获的决策的信息元素。结合依赖性是对不确定事件进行推断或在接收新信息时进行学习的基本步骤，但如果要最小化认知和动机偏差的影响，则需要谨慎地得出具有代表性的概率分布。在推导联合概率分布时，我们面临着额外的困难，如对几个变量的概率评估或评估它们之间的依赖参数。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。提出的研究目标是开发和测试一种使用等概率轮廓（具有相同累积概率的点的轮廓）构建连续随机变量联合概率分布的新方法。我们探索了一种新的方法，通过在二元赌博中引出成对偏好来构建等概率轮廓，而不需要决策者的数字响应。这种方法大大简化了联合概率评估。一旦确定了等概率轮廓和至少一个一维边际概率分布，就有可能构造所有存在变量的联合分布吗？因此，我们也提出了一种利用等概率轮廓来评估决策情境变量之间相关性的新方法。

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.