The aims were twofold. First, to develop a statistical model predicting the probabilities of freedom from Salmonella enterica subspecies enterica serovar Dublin (S. Dublin) antibodies in Danish dairy herds using longitudinal herd-level surveillance data. These data were obtained via antibody-detecting ELISA testing on bulk tank milk (BTM), four times a year. Second, to estimate the sensitivity (Se) and specificity (Sp) of the testing procedure. A total of 8,310 BTM test results from 500 Danish dairy herds were used for this study between 2017 and 2022. These data were combined with prior distributions in a Bayesian Hidden Markov Model ('the STOC free model') to predict herd-level probabilities of antibody presence (and freedom from antibodies). The model fitted the S. Dublin data and gave meaningful results when compared to previous studies and other types of models, i.e., Se = 0.945 (95% credible interval (CI): 0.921-0.962) and Sp = 0.995 (95% CI: 0.992-0.997).