OBJECTIVES: This project examines approaches to the calibration of natural history models from a Bayesian perspective. The result of the calibration is a joint probability distribution of parameters which can be used in a probabilistic analysis (PSA) using a predictive model to compare different interventions. Two diseases are examined. The two models have important differences in terms of the calibration strategies that are employed. The interventions considered for each disease are different too; this affects the choice of model structure. The first disease is HPV, which uses a patient level simulation to account for the transmission dynamic nature of the disease, which is important in considering the impact of herd immunity from vaccination. The second is Hepatitis C, and the purpose of this model is to examine progression of disease and the impact of different strategies for the screen-detected and symptomatic populations. METHODS: Markov Chain Monte Carlo (MCMC) sampling was used to obtain samples from the joint distribution for the unobservable parameters and compared with Monte Carlo approach. RESULTS: The biggest challenge with HPV model calibration was the extensive unparallelisable computational time (20 days of computing time per chain per processor) that was significantly slowing down the calibration process. The non-identifiability of the parameter space had also a great impact on convergence of chains. A solution to the problem was to impose a structural prior on the joint parameter space. The Hepatitis C model calibration was an easier problem. The convergence was quicker, computational time was acceptable and some sensible predictions were achieved. Adaptive MCMC was used for calibrating this model. CONCLUSIONS:  Advantages of MCMC: for HPV — a better fit comparing to simple Monte Carlo method; for Hepatitis C — good exploration of the parameter space. Disadvantages of MCMC: poor mixing and convergence for HPV model; additional computational time for Hepatitis C model.