用相互作用组重构多组居里 - 外斯模型的概率测度
Reconstructing the Probability Measure of a Multi-group Curie-Weiss Model with Interacting Groups
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中文总结 AI 辅助
研究从人群投票行为样本重构多组居里 - 外斯模型概率测度问题，针对多组模型耦合参数估计难题，分析基于渐近近似的估计器，有望应用于政治学、社会学等学科。
中文摘要 AI 辅助
我们研究从人群投票行为样本中重构铁磁居里 - 外斯或平均场模型多组版本概率测度的问题。居里 - 外斯模型最初用于研究统计力学中的相变，现用于研究多主体相互作用现象。多组模型有更多耦合参数需估计，最大似然估计虽理论上有良好统计性质，但计算挑战使其不适用于大群体。因此我们分析基于渐近近似的估计器，因其对居里 - 外斯模型行为有效，该估计器在政治学、社会学等学科可能有用。
英文摘要
We study the problem of reconstructing the probability measure of a multi-group version of the Curie-Weiss or mean-field model of ferromagnetism from a sample of the voting behaviour the population. While originally used to study phase transitions in statistical mechanics, the Curie-Weiss or mean-field model has been applied to study phenomena where many agents interact with each other, in particular in case of a heterogeneous population with identifiable subpopulations. The degree of social cohesion within social groups manifests in the way the members of the group influence each others' decisions as well as how they behave under outside influence from voters belonging to another group. Contrary to single-group Curie-Weiss models, here we have a larger number of coupling parameters which have to be estimated. While the maximum likelihood estimator of the coupling parameters has desirable statistical properties in theory, computational challenges make applications to larger populations impractical. Therefore, we analyse an estimator based on asymptotic approximations to the behaviour of the Curie-Weiss model valid for large populations. Due to the wide applicability of models such as Curie-Weiss, the estimator is potentially useful in disciplines such as political science, sociology, automated voting, and preference aggregation.
