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）备选方案，或我们能做什么;（2）信息，或我们知道什么;（3）偏好，或我们喜欢什么。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替代方案。本研究的重点是信息元素的决定，是由几个变量的联合概率分布捕获。纳入依赖性是对不确定事件进行推断或在我们收到新信息时进行学习的基本步骤，但如果要最大限度地减少认知和动机偏见的影响，则引出代表性概率分布是一项需要谨慎的任务。当引出联合概率分布，我们面临着额外的困难，如条件的概率评估的几个变量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很难执行。拟议的研究的目标是开发和测试一种新的方法，用于构建连续随机变量的联合概率分布，使用等概率轮廓（具有相同累积概率的点的轮廓）。我们探索了一种新的方法来构建等概率轮廓引发成对的偏好超过二进制赌博，而不需要从决策者的数字响应。这种方法大大方便了联合概率评估。一旦确定了等概率分布和至少一个一维边际概率分布，就可以构造所有变量的联合分布。因此，我们还提出了一种新的方法，用于评估决策情况的变量之间的依赖关系，使用等概率轮廓。

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.