Most modern articles in the palaeomagnetism literature are based on statistics developed by Fisher's 1953 paper ‘Dispersion on a sphere’, which assumes independent and identically distributed (iid) spherical data. However, palaeomagnetic sample designs are usually hierarchical, where specimens are collected within sites and the data are then combined across sites to calculate an overall mean direction for a geological formation. The specimens within sites are typically more similar than specimens between different sites, and so the iid assumptions fail. This article has three principal goals. The first is to review, contrast and compare both the statistics and geophysics literature on the topic of analysis methods for clustered data on spheres. The second is to present a new hierarchical parametric model, which avoids the unrealistic assumption of rotational symmetry in Fisher's 1953 paper ‘Dispersion on a sphere’ and may be broadly useful in the analysis of many palaeomagnetic datasets. To help develop the model, we use publicly available data as a case study collected from the Golan Heights volcanic plateau. The third goal is to explore different methods for constructing confidence regions for the overall mean direction based on clustered data. Two bootstrap confidence regions that we propose perform well and will be especially useful to geophysics practitioners.

中文翻译：

---

新旧方向：古地磁学和费舍尔（1953）遇见现代统计学

古地磁文献中的大多数现代文章都是基于 Fisher 1953 年的论文“球体上的离散度”开发的统计数据，该论文假设独立且同分布 (iid) 的球形数据。然而，古地磁样本设计通常是分层的，其中在站点内收集样本，然后跨站点组合数据以计算地质构造的总体平均方向。站点内的样本通常比不同站点之间的样本更相似，因此 iid 假设失败。本文有三个主要目标。首先是回顾、对比和比较关于球体聚类数据分析方法主题的统计和地球物理学文献。二是提出一种新的层次化参数模型，这避免了费舍尔 1953 年论文“球体上的分散”中不切实际的旋转对称假设，并且可能在分析许多古地磁数据集时广泛有用。为了帮助开发该模型，我们使用公开数据作为从戈兰高地火山高原收集的案例研究。第三个目标是探索基于聚类数据为整体平均方向构建置信区域的不同方法。我们建议的两个引导置信区域表现良好，对地球物理学从业者特别有用。第三个目标是探索基于聚类数据为整体平均方向构建置信区域的不同方法。我们建议的两个引导置信区域表现良好，对地球物理学从业者特别有用。第三个目标是探索基于聚类数据为整体平均方向构建置信区域的不同方法。我们建议的两个引导置信区域表现良好，对地球物理学从业者特别有用。