Singularities in bivariate normal mixtures
Abstract We investigate mappings whose components are bivariate normal densities from the perspective of singularity theory. Motivated by the need to understand two-component bivariate normal mixtures, we classify these mappings up to right-left equivalence and characterize them using statistical concepts. Our analysis reveals three distinct types, each with specific geometric properties, and we derive upper bounds on the number of modes in the mixture for each type.
Authors
- Hirotaka Matsumoto
- Yutaro Kabata (ORCID: https://orcid.org/0000-0001-6625-8029)
- Seiichi Uchida (ORCID: https://orcid.org/0000-0001-8592-7566)
- Masao Ueki (ORCID: https://orcid.org/0000-0003-0468-7041)
Institutions
- Kagoshima University (JP)
- University of Nagasaki (JP)
- Kyushu University (JP)
- Nagasaki University (JP)
Publication Details
- Journal
- Information Geometry
- Published
- 2025-10-15
- DOI
- https://doi.org/10.1007/s41884-025-00177-0
- Primary Topic
- Bayesian Methods and Mixture Models
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Japan Society for the Promotion of Science