This paper describes a stochastic epidemic model developed to infer transmission rates of asymptomatic communicable pathogens within a hospital ward. Inference is complicated by partial observation of the epidemic process and dependencies within the data. The epidemic process of nosocomial communicable pathogens can be partially observed by routine swabs testing for the presence of the pathogen. False-negative swab results must be accounted for and make it difficult to ascertain the number of patients who were colonized. Reversible jump Markov chain Monte Carlo methods are used within a Bayesian framework to make inferences about the colonization rates and unknown colonization times. The methods are applied to routinely collected data concerning methicillin-resistant Staphylococcus Aureus in an intensive care unit to estimate the effectiveness of isolation on reducing transmission of the bacterium.