Bayesian taut splines for estimating the number of modes
This provides a novel solution for analysts in fields like sports analytics to better identify subpopulations, though it is incremental as it builds on existing Bayesian and spline techniques.
The paper tackles the problem of estimating the number of modes in a univariate probability density function, presenting a Bayesian method that combines kernel estimators and compositional splines, which outperforms traditional approaches in simulation studies.
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.