Mathematical Sciences: Dealing with Mixed Levels of Uncertainty

本研究计划围绕离散选择、建模和估计方面的三个不同但相关的项目展开。共同的主题是消费者选择行为的建模，以及对揭示的偏好数据集上的消费者行为模型的估计。随着电子扫描仪面板数据的可用，选择模型对于理解消费者行为变得非常重要。例如，这样的模型可以用来评估营销组合对消费者购买行为的影响，以及评估市场上的竞争模式。这项研究中的三个研究项目涉及使用最近开发的模拟估计技术。在第一个项目的模型中，消费者的选择概率是对未观察到的价格和息票价值以及随机偏好冲击的高维积分。因此，必须使用蒙特卡罗方法来模拟模型中的似然函数。在第二个和第三个项目中，动态规划问题的求解和似然函数的构造都需要对价格、偏好冲击等随机过程进行高维积分。在这些项目中，我们将使用蒙特卡罗方法来求解消费者的动态规划问题和模拟似然函数。

This research program revolves around three different but related projects in discrete choice modeling and estimation. The common theme is the modeling of consumer choice behavior, and the estimation of models of consumer behavior on revealed preference data sets. With the availability of electronic scanner panel data, choice models have become very important for understanding consumer behavior. For example, such models may be used to evaluate the impact of the marketing mix on consumer purchasing behavior, and to assess the patterns of competition in the market place. The three research projects in this study involve the use of recently developed simulation estimation techniques. In the model of the first project, consumer choice probabilities are high dimensional integrals over unobserved prices and coupon values, as well as over stochastic preference shocks. Thus, Monte-Carlo methods must be used to simulate the likelihood function in the model. In the second and third projects, both solution of the dynamic programming problem and construction of the likelihood function require high dimensional integrations over stochastic process for prices, preference shocks, etc. In these projects we will use Monte- Carlo methods both to solve consumers' dynamic programming problems and to simulate the likelihood function.