Figure 3 An illustrative theoretical example that shows how the mathematical framework will be used to fit the model, estimate an intervention parameter and estimate the impact of the intervention with uncertainty (fig 2). A transmission dynamics model was used to simulate HIV prevalence data (“the truth”) among female sex workers (FSW) and clients in 2004 and 2007. Condom use is assumed to increase from 22% to 80% after the introduction of an intervention in 2005. (A) Results of the model fit for FSW only (clients not shown) using a target method: the prior distributions of each of the 16 model parameters were defined using a reasonable range. A total of 500 000 parameter sets were sampled and tested. Model prediction for each set was compared with the “true” prevalence; 2061 parameter sets fitted the “true” HIV prevalence well, ie fell within the confidence interval (assuming a sample of 400) of the true data points. (B) Resulting posterior distribution of plausible condom use parameter values (representing fraction of sex acts protected) suggested by the fitting procedure, condom use estimates vary between 50% and 90%, with values between 75% and 90% being more likely. The “true” value is 80%. (C) Resulting posterior distribution of new HIV infections averted over five years after the intervention using the 2061 parameter sets that fitted the data well. Most likely model estimates are between 800 and 1400 new infections averted. The true value is 1125. If the validation data (ie HIV prevalence) were more precise (narrower confidence intervals) the fitting procedure would produce more precise parameter and impact estimates. By using priors reflecting different beliefs on parameter or model assumptions, it is also possible to test different hypotheses of prior beliefs in a scientific and objective fashion. The posterior distributions resulting (through the fitting procedure) from the different priors will produce new impact estimates and permit assessment of the sensitivity of our results to different assumptions.