基于对称识别方法的贝叶斯probit模型稳健性研究

Probit models are effective tools to deal with discrete choice data. Especially, recent advances in Bayesian computation have made probit models to be widely used in many areas, such as transportation, economics and marketing. However, parameter identification is an unavoidble topic to fit probit models. New studies find that Bayesian posterior predictions of the multinomial probit model based on traditional identification method are sensitive to the relabeling of alternatives. Then a new identification method, called symmetric identification, was proposed to solve such sensitivity problem. Based on symmetric identification, Baysian inferences on the multinomial probit model are robust enough. Due to the advent of ranking data and multiperiord choice data, the multinomial probit model can't effectively deal with them. Moreover, the existing probit models to deal with such data maily focus on the feasibility of model fitting, overlooking the reliability of predictions. Let alone the robust analysis of the corresponding models with respect to identification methods. Based on symmetric identification, this project mainly study on the robust analysis of Bayesian inferencs on two probit models: the censored rank-ordered probit model and the multiperiod probit model.

Probit模型是处理离散选择问题的一个有力工具，特别是近年来贝叶斯计算的快速发展，使得probit模型获得广泛应用。但是probit模型使用时存在参数识别问题。最新研究发现在用贝叶斯方法处理基于经典识别方法的多项probit模型时出现模型推断关于选择对象的标号敏感。接着有研究提出了对称识别方法，并基于此识别法建立多项probit模型以及进行贝叶斯分析，发现推断结果不依赖于标号变化，非常稳健。随着实际应用中排序数据、多期选择数据的出现，多项probit模型已不能满足需要，另外，目前关于这两种数据的probit模型研究主要集中在分析的便利性方面，而与识别方法相关的模型推断的稳健性还是空白。本项目主要对基于对称识别方法的删失排序probit模型和多期多项probit模型进行贝叶斯推断的稳健性研究，另外研究这两种模型在实际中的应用。

贝叶斯多项probit模型广泛用于分析规则的离散选择数据。最新研究发现由现有的模型所产生的后验预测对被选择对象的标号有敏感性，即不同的人为标号会导致不同的预测结果。对于规则数据，我们已经提出了全局对称识别模型有效解决了贝叶斯后验预测的敏感性问题。随着网络和计算机技术的发展，产生了大量的复杂选择数据，比如删失排序数据，多期多项选择数据。本项目的任务是利用对称识别方法建立稳健的贝叶斯probit模型来处理这些复杂的选择数据。对于删失排序数据，我们已经建好了贝叶斯删失排序probit模型，基于这个模型可以得到稳健的后验预测结果。另外，还将此模型用于分析香港赛马数据，发现模型给出预测与真实结果吻合很好。