Cancer natural history models are essential when evaluating screening interventions, preventative interventions or changes to diagnostic pathways. Natural history models commonly use a state transition structure where the progression of disease is split into distinct disease states but it is often not possible to directly observe the state transition probabilities required to parameterise such a model. An existing Excel markov state transition model for the natural history of colorectal cancer (CRC) was modified and updated with recent English data. The work aimed to accurately represent the uncertainty in natural history parameters by embedding the problem in the framework of Bayesian inference. The Metropolis-Hastings algorithm was used to estimate natural history parameters by generating multiple sets of parameters from the posterior distribution, which is a probability distribution that is compatible with the observed data.  Observed data included incidence categorised by age and stage, autopsy data on polyp prevalence, and cancer and polyp detection rates from the first round of screening. The approach was implemented using Visual Basic within the EXCEL model and the results were subsequently examined for convergence using the package CODA in R 2.8.0. Outputs from the fitting process were samples from the joint posterior distribution of the natural history parameters given the epidemiological data. These parameter sets are used when running PSA. The advantages of this strategy are that it draws efficiently (compared to simple Monte Carlo or Latin Hypercube) from a high dimensional correlated parameter space. The underlying methodology is well developed in the Bayesian literature. The algorithm is simple to code and could be run overnight on a standard desktop PC. Using this method the parameter sets are drawn according to their posterior probability given calibration data and thus they correctly summarise the residual uncertainty in the parameter space given the data that are available.