Efficient Bayesian Synthetic Likelihood with Whitening Transformations

Simulator models are utilised extensively to improve our understanding of complex phenomena. Some recent applications include: in biology, to model the spread of the Banana Bunchy Top Virus; in epidemiology, to model the transmission of HIV and tuberculosis, and, in ecology, to model the dispersal of Little owls. By calibrating a model to an observed dataset, we are able to link our hypothesised model to the real world. However, for these types of models, it is often difficult to express the model as a mathematical formula, precluding the use of classical statistical methods for model calibration. 

In this setting, likelihood-free inference methods, such as approximate Bayesian computation (ABC) and Bayesian synthetic likelihood (BSL) may be employed for statistical inference. However, these methods are computationally expensive as they rely on simulating a large number of pseudo datasets from the model. 

In this new paper, we introduce a new method which significantly improves the computational efficiency of BSL. We demonstrate the efficacy of our method on a range of simulated and real modelling scenarios from ecology and biology.