= Mixture identifiability
Simultaneously applying a <permutation> to the <mixture weights> and <mixture components> leaves $f$ unchanged. Thus <identifiability> of named components requires a convention, such as ordering distinct component <means>; <label switching> describes the associated inferential issue.<Advanced Data Analysis from an Elementary Point of View, 2015 draft by Cosma Rohilla Shalizi/Mixture Models>[§21.1.5, printed pp. 444-445: observational equivalence and label degeneracy]{ref}
Even after choosing label names, identical <mixture components> reveal only their combined <mixture weight>, and an inactive <mixture component> has undetermined <statistical parameters>. Adding <mixture components> increases flexibility but can cause <overfitting>; judge predictions using <cross-validation>, rather than interpreting every fitted component as a discovered population.<Advanced Data Analysis from an Elementary Point of View, 2015 draft by Cosma Rohilla Shalizi/Mixture Models>[§21.1.6, printed pp. 445-446: probabilistic clustering and evaluation on future data]{ref}
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