部分识别离散响应模型的非参数贝叶斯推断
Nonparametric Bayesian Inference for Partially Identified Discrete Response Models
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中文总结 AI 辅助
本文提出部分识别离散响应模型的非参数贝叶斯推断框架，其后验相合且计算简便，可扩展至多类响应场景。
中文摘要 AI 辅助
本文提出了一种针对部分识别离散响应模型的非参数贝叶斯推断框架。关键观察在于，这类模型将简化形式的条件选择概率映射到一个识别集。因此，对条件概率质量函数的非参数贝叶斯推断，可转化为对该识别集的贝叶斯推断。该推断框架将条件矩不等式和含未知系数的线性系统作为特例包含在内。重要的是，本文所提方案无需将条件矩转化为无条件矩，也无需对协变量进行离散化。研究表明，当模型设定正确时，后验分布对真实识别集是相合的；后验分布可一致地检测模型设定误；后验分布对设定误下仍有效的伪识别集也具有相合性。本文还验证了用于实现该方案的一类基于高斯过程的先验的假设。这些先验提供了与频率论部分识别方法相似的灵活性，且计算上具有吸引力，因为后验抽样可闭式进行。此外，本文还表明，该文的许多思路可扩展至连续响应和聚合离散响应（如市场份额）。
英文摘要
This paper proposes a nonparametric Bayesian inference framework for partially identified discrete response models. The key observation is that these models map a reduced-form conditional choice probability to an identified set. Consequently, nonparametric Bayesian inference for the conditional probability mass function leads to Bayesian inference for the identified set. The inference framework nests conditional moment inequalities and linear systems with unknown coefficients as special cases. Importantly, our proposal does not require converting conditional moments into unconditional moments or discretizing covariates. We show that the posterior is consistent for the true identified set when the model is correctly specified, show that the posterior can consistently detect model misspecification, and show posterior consistency for a pseudo-identified set that is valid under misspecification. We also verify the assumptions for a class of priors based on Gaussian processes that we use to implement our proposal. These priors offer similar flexibility to frequentist partial identification methods, and are computationally attractive because posterior sampling can be performed in closed-form. We also show that many of the ideas in this paper extend to continuous responses and aggregated discrete responses (e.g., market shares).
