This paper develops a statistical framework for a retrospective analysis for well-observed livestock epidemics during which intervention policies may conceal cases, thus potentially biasing naively derived parameter and final size estimates. We apply the methods to the 2001 foot and mouth epidemic (FMD) in Great Britain, during which a large number of farms (about 7500) were pre-emptively culled as part of the control effort without ever being diagnosed as being infected. We infer farm-level infectivity and susceptibility parameters, a distribution for the delay from infection to report, together with a time varying farm infectivity profile for farms. Hidden infections among proactively culled farms were accounted for using a data augmentation approach utilising reversible jump MCMC methods. Simulated epidemics derived using the parameter estimates obtained reproduced the 2001 epidemic well. Our analysis demonstrates that time-varying infectivity profiles fit the 2001 data better than naive assumptions of constant infectiousness. We estimate that around 210 (or 2.8%) of the farms proactively culled in the 2001 epidemic were infected. However, for the parameter estimated obtained, preliminary simulation results indicate that had contiguous culling not been applied in 2001, the epidemic might have been substantially larger.