A Bayesian two-component mixture model for predicting low and high coagulase-positive staphylococci contamination levels in raw milk

In this study, we developed a Bayesian two-component Gaussian mixture model to predict coagulase-positive staphylococci (CPS) concentration in raw milk and estimate the posterior probability of belonging to latent low- and high-CPS contamination levels. Thirty-six raw milk samples were collected through longitudinal sampling of 12 raw-milk batches. CPS, total bacterial count (TBC), lactic acid bacteria (LAB), somatic cell count, milk protein and fat content, and pH were quantified, while rainfall, environmental temperature and relative humidity were recorded. Missing TBC and LAB values were handled using Bayesian model-based imputation. The final pH-extended mixture model showed satisfactory Markov Chain Monte Carlo diagnostics and adequately reproduced the observed non-unimodal CPS distribution, with 93.3% of posterior predictive replicated datasets showing at least two modes. TBC was positively associated with the low-CPS contamination component, whereas pH showed a weak negative tendency in the high-CPS contamination component. Prior sensitivity analysis indicated that the main findings were stable under stronger prior regularization. These findings demonstrate the feasibility of a regularized Bayesian mixture modelling framework for probabilistic CPS prediction in raw milk. External validation is required before the model can be considered operational. To support its application, a userfriendly web-based prediction tool has been developed.