Evidence accumulation models (EAMs) are widely used to model decision-making data. Here, model parameter estimation requires an evaluation of the model likelihood. However, as EAMs become more complex, analytical likelihood evaluation becomes increasingly costly or intractable. This computational cost accumulates in Bayesian inference involving Markov chain Monte Carlo as the likelihood needs to be evaluated repeatedly. Simulation-based inference (SBI) has been applied to gain access to intractable likelihoods. We conducted a large-scale comparison of two SBI approaches—kernel density estimation (KDE) and neural likelihood estimation (NLE)—in their ability to efficiently approximate EAM likelihoods.

To this end, we simulated data from three EAMs of increasing complexity: the log-normal race, the racing diffusion model and the full diffusion decision model (DDM). While the racing models have an efficient analytical likelihood, the likelihood of the full DDM requires a numerical approximation of a multidimensional integral. NLE and KDE were trained on increasing simulation budgets for each model. 

Results showed that NLE approximated the model likelihoods better than KDE, while also being more computationally efficient. Additionally, although slower than the analytical racing model likelihoods, evaluation of the NLE model was orders of magnitude faster than the numerical approximation of the full DDM likelihood. Although kernel density evaluation was also faster than the numerical approximation, it incurred substantial overhead because it must be refit to each new parameter set. In contrast, NLE learns a smooth function over the parameter space and therefore generalises to unseen parameter values.

Overall, NLE can allow for fast and accurate likelihood approximation, especially for the full DDM. Further, NLE models can be re-used without additional training cost. Future research should investigate parameter recovery using NLE, so these benefits can ultimately be leveraged in full Bayesian inference pipelines.