We present a Bayesian approach to predict the clustering of opinions for a system of interacting agents from partial observations. The Bayesian formulation overcomes the unobservability of the system and quantifies the uncertainty in the prediction. We characterize the clustering by the posterior of the clusters’ sizes and centers, and we represent the posterior by samples. To overcome the challenge in sampling the high-dimensional posterior, we introduce an auxiliary implicit sampling (AIS) algorithm using two-step observations. Numerical results show that the AIS algorithm leads to accurate predictions of the sizes and centers for the leading clusters, in both cases of noiseless and noisy observations. In particular, the centers are predicted with high success rates, but the sizes exhibit a considerable uncertainty that is sensitive to observation noise and the observation ratio.

中文翻译：

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基于局部观测的观点动态聚类预测

我们提出了一种贝叶斯方法来预测来自部分观察值的交互代理系统的观点聚集。贝叶斯公式克服了系统的不可观测性，并量化了预测中的不确定性。我们通过聚类的大小和中心的后验来表征聚类，并通过样本来表示后验。为了克服对高维后验采样的挑战，我们引入了使用两步观测的辅助隐式采样（AIS）算法。数值结果表明，在无噪声和嘈杂观测的情况下，AIS算法都能精确预测领先星团的大小和中心。特别是，这些中心的成功率很高，