The primary objective of this dissertation is to utilise, adapt and extend current stochastic models and statistical inference techniques to describe the transmission of nosocomial pathogens, i.e. hospital-acquired pathogens, and multiply-resistant organisms within the hospital setting. The emergence of higher levels of antibiotic resistance is threatening the long term viability of current treatment options and placing greater emphasis on the use of infection control procedures. The relative importance and value of various infection control practices is often debated and there is a lack of quantitative evidence concerning their effectiveness. The methods developed in this dissertation are applied to data of methicillin-resistant Staphylococcus aureus occurrence in intensive care units to quantify the effectiveness of infection control procedures. Analysis of infectious disease or carriage data is complicated by dependencies within the data and partial observation of the transmission process. Dependencies within the data are inherent because the risk of colonisation depends on the number of other colonised individuals. The colonisation times, chain and duration are often not visible to the human eye making only partial observation of the transmission process possible. Within a hospital setting, routine surveillance monitoring permits knowledge of interval-censored colonisation times. However, consideration needs to be given to the possibility of false negative outcomes when relying on observations from routine surveillance monitoring. SI (Susceptible, Infected) models are commonly used to describe community epidemic processes and allow for any inherent dependencies. Statistical inference techniques, such as the expectation-maximisation (EM) algorithm and Markov chain Monte Carlo (MCMC) can be used to estimate the model parameters when only partial observation of the epidemic process is possible. These methods appear well suited for the analysis of hospital infectious disease data but need to be adapted for short patient stays through migration. This thesis focuses on the use of Bayesian statistics to explore the posterior distributions of the unknown parameters. MCMC techniques are introduced to overcome analytical intractability caused by partial observation of the epidemic process. Statistical issues such as model adequacy and MCMC convergence assessment are discussed throughout the thesis. The new methodology allows the quantification of the relative importance of different transmission routes and the benefits of hospital practices, in terms of changed transmission rates. Evidence-based decisions can therefore be made on the impact of infection control procedures which is otherwise difficult on the basis of clinical studies alone. The methods are applied to data describing the occurrence of methicillin-resistant Staphylococcus aureus within intensive care units in hospitals in Brisbane and London