Random mixtures in Bayes Hilbert spaces
Abstract
We present a framework for the analysis and unmixing of random density mixtures in the Bayes Hilbert space. General identifiability results for mixtures in Hilbert spaces are established and applied to the Bayes Hilbert space setting. Building on these results, we propose a penalised maximum likelihood approach for the unmixing of Bayes Hilbert mixtures aimed at recovering the statistically space-efficient representation, together with a computationally efficient coordinate-wise maximisation algorithm for its implementation. The methodology is illustrated through a hyperspectral data application, where observations can be naturally embedded in the Bayes Hilbert space and analyzed in terms of distributional shape rather than amplitude. A complementary simulation study demonstrates the interpretability and practical performance of the proposed approach.
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BibTeX
@misc{patane2026random,
title = {{Random mixtures in Bayes Hilbert spaces}},
author = {Giulia Patanè and Sonja Greven and Alessandra Menafoglio},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03523},
eprint = {2609.03523},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03523},
}
RIS
TY - UNPB
TI - Random mixtures in Bayes Hilbert spaces
AU - Giulia Patanè
AU - Sonja Greven
AU - Alessandra Menafoglio
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.03523
UR - https://arxiv.org/abs/2609.03523
AB - We present a framework for the analysis and unmixing of random density mixtures in the Bayes Hilbert space. General identifiability results for mixtures in Hilbert spaces are established and applied to the Bayes Hilbert space setting. Building on these results, we propose a penalised maximum likelihood approach for the unmixing of Bayes Hilbert mixtures aimed at recovering the statistically space-efficient representation, together with a computationally efficient coordinate-wise maximisation algorithm for its implementation. The methodology is illustrated through a hyperspectral data application, where observations can be naturally embedded in the Bayes Hilbert space and analyzed in terms of distributional shape rather than amplitude. A complementary simulation study demonstrates the interpretability and practical performance of the proposed approach.
ER -