There are numerous statistics solutions dedicated to hyperspectral classification (considered from the "target detection" point of view) based on hypothesis testing. Examples include, but are not limited to, the following ones:
C.-I Chang, "Statistical Detection Theory Approach to Hyperspectral Image Classification", 2018 -
Article Statistical Detection Theory Approach to Hyperspectral Image...
C.-I Chang et al., "Target Detection Approaches to Hyperspectral Image Classification", Chapt. 20, 2022 -
Chapter Target Detection Approaches to Hyperspectral Image Classification
He et al., "Instance-Based Classification Through Hypothesis Testing", 2021 - https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=9333560