Bayesian taut splines for estimating the number of modes

TL;DR

This paper introduces a Bayesian spline-based method for accurately estimating the number of modes in univariate probability densities, addressing limitations of traditional approaches and incorporating expert judgment.

Contribution

It presents a novel Bayesian approach combining kernel estimators and splines to estimate modes, with a focus on structure, uncertainty, and holistic density analysis.

Findings

Outperforms traditional modality-driven methods in accuracy

Provides soft, expert-informed solutions for mode estimation

Includes comprehensive visualization tools and case studies

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.