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arXiv · 2410.00415

Singularities in bivariate normal mixtures

Yutaro Kabata·Hirotaka Matsumoto·Seiichi Uchida·Masao Ueki
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Abstract

We investigate mappings $F = (f_1, f_2) \colon \mathbb{R}^2 \to \mathbb{R}^2 $ where $ f_1, f_2 $ are bivariate normal densities from the perspective of singularity theory of mappings, motivated by the need to understand properties of two-component bivariate normal mixtures. We show a classification of mappings $ F = (f_1, f_2) $ via $\mathcal{A}$-equivalence and characterize them using statistical notions. Our analysis reveals three distinct types, each with specific geometric properties. Furthermore, we determine the upper bounds for the number of modes in the mixture for each type.

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Yutaro Kabata, Hirotaka Matsumoto, Seiichi Uchida, Masao Ueki. 2024-10-01. Singularities in bivariate normal mixtures. https://arxiv.org/abs/2410.00415

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