Introduction The complexity of dynamic epidemic systems has led to the use of large-scale stochastic models for prediction purposes. However, methods for robustly calibrating and analysing these models can be prohibitively inefficient. We propose an algorithm for fitting complex models that incorporates elements of both Approximate Bayesian Computation (ABC) and Bayesian Emulation. ABC enables inference about model parameters without needing to calculate a likelihood function, by generating approximations from repeated model runs. However, each model run might take hours. Emulation methods are being developed in the fields of cosmology and meteorological modelling. The complex model function is summarised as an “emulator”: a stochastic function that represents global behaviour of the function as a linear regression model and local deviations from this behaviour as Gaussian processes. The emulator acts as a cheap proxy for the complex model, allowing both calibration and sensitivity analysis to be conducted in a fraction of the time.
Methods We report the initial application of an emulation-based calibration algorithm to an individual-based stochastic model of STI transmission in Uganda. Starting with uninformative priors for 19 behavioural and biological input parameters, we “trained” an emulator with 200 sampled parameter sets and their corresponding model output (point estimates of HIV prevalence). Sampling a further 10 000 parameter sets from the priors, we used the emulator to make output predictions over a large area of input parameter space. Weighting each parameter set by goodness of fit to observed data, we identified promising areas of parameter space for complex model evaluation. A more accurate emulator was then trained, incorporating this additional complex model output. The process was repeated as in sequential ABC methods.
Results The use of emulators allowed evaluation of large areas of parameter space due to increased computational efficiency. Processing time for one prevalence point estimate was reduced from over 15 min on an HPC cluster to less than 0.1 s on a PC. Even the first two waves of such an algorithm provided helpful insight into the most influential parameters.
Conclusions The development of an ABC—Bayesian Emulation hybrid approach to complex model calibration is promising. Emulators offer large advantages in computational efficiency. However, further research is needed regarding weighting, tolerance levels and covariance.