Bayesian mixture models are a standard tool when data come from multiple latent populations, but they assume the model is correctly specified for every component. In practice, some populations may be poorly understood or irrelevant to the research question, and a misspecified component can bias posterior estimates for the parameters that actually matter. Autenrieth et al. propose a modular Bayesian framework that explicitly protects the target inference from such contamination.
Instead of jointly fitting the full mixture, the method first obtains fixed class probabilities—for example from a classifier trained on labelled data—and uses them to decouple classification from downstream analysis. The likelihood contributions of less trustworthy populations are then prevented from influencing the protected parameters. This modularization also simplifies computation: the full joint analysis reduces to sampling label allocations, fitting the protected downstream model for each sample, and averaging the resulting posteriors.
The authors establish calibration conditions on the class probabilities under which the procedure preserves the inferential target that would be obtained with known labels. They demonstrate the approach in synthetic experiments and in a cosmological analysis of photometric supernova samples. The work offers a principled way to handle uncertain class labels while guarding against model misspecification in the components that are not the focus of inference.