Simulated training dataset (top) and predicted posterior probabilities of the three models (bottom)
Abstract
A common problem in computational neuroscience is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for the data. In practice, however, models are often defined through complex simulators so that methods relying on likelihood functions are not applicable. Previous approaches in the field of Approximate Bayesian Computation (ABC) rely on rejection sampling to circumvent the likelihood, but are typically computationally inefficient. We propose an efficient method to perform Bayesian model comparison for simulation-based models. Using recent advances in posterior density estimation, we train a mixture-density network to map features of the observed data to the parameters of the posterior over models. We show that the method performs accurately on two tractable example problems, and present an application to a use case scenario from computational neuroscience – the comparison of ion channel models.