We develop a simple, yet powerful, technique based on linear regression models of parametrized closed curves which induces a probability distribution on the planar shape space. Such parametrization is driven by control points which can be estimated from the data. Our proposal is capable to infer about the mean shape, to predict the shape of an object at an unobserved location, and, while doing so, to consider the effect of predictors on the shape. In particular, the model is able to detect possible differences across the levels of the predictor, thus also applicable for two-sample tests. A simple MCMC algorithm for Bayesian inference is also presented and tested with simulated and real datasets. Supplementary material is available online.

中文翻译：

---

基于参数化闭合曲线的统计形状分析线性模型

我们开发了一种基于参数化闭合曲线的线性回归模型的简单而强大的技术，该模型在平面形状空间上产生概率分布。这种参数化由可以从数据中估计的控制点驱动。我们的提议能够推断平均形状，预测未观察到的位置的物体形状，并在这样做的同时考虑预测因子对形状的影响。特别是，该模型能够检测预测变量水平之间可能存在的差异，因此也适用于双样本检验。还介绍了一种用于贝叶斯推理的简单 MCMC 算法，并使用模拟和真实数据集进行了测试。补充材料可在线获得。