Bayesian taut splines for estimating the number of modes
提出一种结合核估计与组合样条的贝叶斯方法，用于估计单变量概率密度函数的模态数量，通过软解和专家知识提升预测准确性，在模拟和体育分析案例中优于传统方法。
The number of modes in a probability density function is representative of the complexity of a model and can also be viewed as the number of subpopulations. Despite its relevance, there has been limited research in this area. A novel approach to estimating the number of modes in the univariate setting is presented, focusing on prediction accuracy and inspired by some overlooked aspects of the problem: the need for structure in the solutions, the subjective and uncertain nature of modes, and the convenience of a holistic view that blends local and global density properties. The technique combines flexible kernel estimators and parsimonious compositional splines in the Bayesian inference paradigm, providing soft solutions and incorporating expert judgment. The procedure includes feature exploration, model selection, and mode testing, illustrated in a sports analytics case study showcasing multiple companion visualisation tools. A thorough simulation study also demonstrates that traditional modality-driven approaches paradoxically struggle to provide accurate results. In this context, the new method emerges as a top-tier alternative, offering innovative solutions for analysts. • Combining kernel estimators and compositional splines benefits mode exploration. • Dimensionality reduction with one principal component captures the essential modes. • Bayesian inference admits expert knowledge regarding modality in soft solutions. • The new proposal and other generic methods outperform classic modality approaches.