论文标题
使用预测递归估算球体上的混合分布
Estimating a mixing distribution on the sphere using predictive recursion
论文作者
论文摘要
当数据显示异质性的迹象时，通常使用混合模型，并且通常估计负责该异质性的潜在变量的分布非常重要。这对于在欧几里得空间中获取值的数据是一个常见的问题，但是基于定向数据在单位球上取值的分布估算的工作受到限制。在本文中，我们建议使用预测递归（PR）算法求解球体上的混合物。 PR的一个关键特征是其计算效率。此外，与仅支持有限混合分布估计值的基于似然的方法相比，PR能够估计平滑的混合密度。建立了PR在球形混合物模型中的渐近一致性，与现有基于可能性的方法相比，模拟结果展示了其优势。我们还展示了两个真正的数据示例，以说明如何将PR用于合适的测试和聚类。
Mixture models are commonly used when data show signs of heterogeneity and, often, it is important to estimate the distribution of the latent variable responsible for that heterogeneity. This is a common problem for data taking values in a Euclidean space, but the work on mixing distribution estimation based on directional data taking values on the unit sphere is limited. In this paper, we propose using the predictive recursion (PR) algorithm to solve for a mixture on a sphere. One key feature of PR is its computational efficiency. Moreover, compared to likelihood-based methods that only support finite mixing distribution estimates, PR is able to estimate a smooth mixing density. PR's asymptotic consistency in spherical mixture models is established, and simulation results showcase its benefits compared to existing likelihood-based methods. We also show two real-data examples to illustrate how PR can be used for goodness-of-fit testing and clustering.
