Random mixtures in Bayes Hilbert spaces

2026-09-03

AI Summary

本文提出了一种在贝叶斯希尔伯特空间中分析和分解随机密度混合物的方法，采用惩罚最大似然法并结合坐标式最大化算法实现。

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.

Problem

• random density mixtures
• Bayes Hilbert space
• unmixing
• identifiability
• hyperspectral data

Innovation

• Bayes Hilbert space
• random density mixtures
• penalised maximum likelihood
• coordinate-wise maximisation algorithm
• hyperspectral data