Fan Jianqing, Tong Xin, Zeng Yao
Frederick L. Moore'18 Professor of Finance, Department of Operations Research and Finance Engineering, Princeton University, Princeton, NJ 08544 (
Marshall School of Business, University of Southern California, CA 90089 (
J Am Stat Assoc. 2015;110(509):149-158. doi: 10.1080/01621459.2014.893885. Epub 2015 Apr 22.
When people in a society want to make inference about some parameter, each person may want to use data collected by other people. Information (data) exchange in social networks is usually costly, so to make reliable statistical decisions, people need to trade off the benefits and costs of information acquisition. Conflicts of interests and coordination problems will arise in the process. Classical statistics does not consider people's incentives and interactions in the data collection process. To address this imperfection, this work explores multi-agent Bayesian inference problems with a game theoretic social network model. Motivated by our interest in aggregate inference at the societal level, we propose a new concept, , to address whether with high probability, a large fraction of people in a given finite population network can make "good" inference. Serving as a foundation, this concept enables us to study the long run trend of aggregate inference quality as population grows.
当社会中的人们想要对某个参数进行推断时，每个人可能都想使用其他人收集的数据。社交网络中的信息（数据）交换通常成本高昂，因此为了做出可靠的统计决策，人们需要权衡信息获取的收益和成本。在此过程中会出现利益冲突和协调问题。经典统计学没有考虑人们在数据收集过程中的动机和相互作用。为了解决这一缺陷，这项工作利用博弈论社会网络模型探索多智能体贝叶斯推断问题。出于我们对社会层面总体推断的兴趣，我们提出了一个新概念，即 ，以解决在给定的有限总体网络中，是否有很大一部分人能够以高概率做出“良好”推断的问题。作为一个基础，这个概念使我们能够研究随着总体规模的增长，总体推断质量的长期趋势。
