Bayesian taut splines for estimating the number of modes

José E. Chacón and Javier Fernández Serrano

Computational Statistics & Data Analysis, 2024, vol. 196, issue C

Abstract: 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.

Keywords: Number of modes; Bayesian inference; Compositional spline; Kernel density estimation; Model selection; Mode testing (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:196:y:2024:i:c:s0167947324000458

DOI: 10.1016/j.csda.2024.107961

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