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Multi-species occupancy (MSO) models use detection-nondetection data from species observed at different locations to estimate the probability that a particular species occupies a particular geographical region. The models are particularly useful for estimating the occupancy probabilities associated with rare species since they are seldom observed when undertaking field surveys. In this paper, we develop Gibbs sampling algorithms that can be used to fit various Bayesian MSO models to detection-nondetection data. Bayesian analysis of these models can be undertaken using statistical packages such as JAGS, Stan, and NIMBLE. However, since these packages were not developed specifically to fit occupancy models, one often experiences long run-times when undertaking analysis. However, we find that these packages that were not developed specifically to fit MSO models are less efficient than our special …