Abstract
Race models describe speeded decision-making as a race between competing runners that accumulate evidence in favor of available choice options. Their parameters can be estimated through the model likelihood that combines the probability and cumulative density functions of each runner. However, estimating parameters of complex race models whose runners have intractable densities with (hierarchical) Bayesian inference has been challenging: Numerical density approximations tend to be slow and amortized neural posterior estimation methods require complex network architectures that can be expensive to train and, in classical settings, tie the trained estimator to a specific prior distribution and generative model. We propose a flexible neural estimation method that decouples training from the choice of prior distribution or model parameterization. We train a small neural network together with a monotonic neural spline flow to simultaneously learn the runners' conditional probability density and cumulative density functions. We then combine both functions to efficiently estimate race model likelihoods that can be used in combination with modern samplers. We demonstrate the utility of our approach on both tractable and intractable versions of the popular racing diffusion model. Based on our results, we argue that, when flexibility in choosing prior distributions or model parameterizations is needed, learning the model likelihood with lightweight neural density estimators is advantageous.