Calibration of models to data: a comparison of methods
Authors: Suboi Zenabu , Hladish Thomas J. , Delva Wim , Hazelbag C. Marijn 
Published: December 2020

Complex models are often fitted to data using simulation-based calibration, a computationally challenging process. Several calibration methods to improve computational efficiency have been developed with no consensus on which methods perform best. We did a simulation study comparing the performance of 5 methods that differed in their Goodness-of-Fit (GOF) metrics and parameter search strategies. Posterior densities for two parameters of a simple Susceptible-Infectious-Recovered epidemic model were obtained for each calibration method under two scenarios. Scenario 1 (S1) allowed 60K model runs and provided two target statistics, whereas scenario 2 (S2) allowed 75K model runs and provided three target statistics. For both scenarios, we obtained reference posteriors against which we compare all other methods by running Rejection ABC for 5M parameter combinations, retaining the 0.1% best. We assessed performance by applying a 2D-grid to all posterior densities and quantifying the percentage overlap with the reference posterior.

We considered basic and adaptive sampling calibration methods. Of the basic calibration methods, Bayesian calibration (Bc) Sampling Importance Resampling (S1: 34.8%, S2: 39.8%) outperformed Rejection Approximate Bayesian Computation (ABC) (S1: 2.3%, S2: 1.8%). Among the adaptive sampling methods, Bc Incremental Mixture Importance Sampling (S1: 72.7%, S2: 85.5%) outperformed sequential Monte Carlo ABC (AbcSmc) (S1: 53.9%, S2: 72.9%) and Sequential ABC (S1: 21.6%, S2: 62.7%).

Basic methods led to sub-optimal calibration results. Methods using the surrogate Likelihood as a GOF outperformed methods using a distance measure. Adaptive sampling methods were more efficient compared to their basic counterparts and resulted in accurate posterior distributions. BcIMIS was the best performing method. When three rather than two target statistics were available, the difference in performance between the adaptive sampling methods was less pronounced. Although BcIMIS outperforms the other methods, limitations related to the target statistics and available computing infrastructure may warrant the choice of an alternative method.

Author summary

As mathematical models become more realistic, they tend to become more complex. Calibration, the process of tuning a model to better reproduce empirical data, can become dramatically more computationally intensive as model complexity increases. Researchers have responded by developing a range of more efficient, adaptive sampling calibration methods. However, the relative performance of these calibration methods remains unclear. To this end, we quantified the performance of five commonly used calibration methods. We found that adaptive sampling methods were more efficient compared to their basic counterparts and resulted in more accurate posterior distributions. We identified the best performing method, but caution that limitations related to the target statistics and available computing infrastructure may warrant the choice of one of the alternatives. Finally, we provide the code used to apply the calibration methods in our study as a primer to facilitate their application.