基于对称识别方法的贝叶斯probit模型稳健性研究

项目名称： 基于对称识别方法的贝叶斯probit模型稳健性研究

项目编号： No.11501287

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 潘茂林

作者单位： 南京大学

项目金额： 18万元

中文摘要： 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。

中文关键词： probit模型；贝叶斯计算；Gibbs抽样；数据扩充；离散选择模型

英文摘要： 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.

英文关键词： probit model;Bayesian computation;Gibbs sampling;data augmentation;discrete choie model