Efficient Inference in First Passage Time Models.

First passage time models describe the time it takes for a random process to exit a region of interest and are widely used across various scientific fields. Fast and accurate numerical methods for computing the likelihood function in these models are essential for efficient statistical inference of model parameters. Specifically, in computational cognitive neuroscience, generalized drift diffusion models (GDDMs) are an important class of first passage time models that describe the latent psychological processes underlying simple decision-making scenarios. GDDMs model the joint distribution over choices and response times as the first hitting time of a one-dimensional stochastic differential equation (SDE) to possibly time-varying upper and lower boundaries. They are widely applied to extract parameters associated with distinct cognitive and neural mechanisms. However, current likelihood computation methods struggle in common application scenarios in which drift rates dynamically vary within trials as a function of exogenous covariates (e.g., brain activity in specific regions or visual fixations). In this work, we propose a fast and flexible algorithm for computing the likelihood function of GDDMs based on a large class of SDEs satisfying the Cherkasov condition. Our method divides each trial into discrete stages, employs fast analytical results to compute stage-wise densities, and integrates these to compute the overall trial-wise likelihood. Numerical examples demonstrate that our method not only yields accurate likelihood evaluations for efficient statistical inference, but also considerably outperforms existing approaches in terms of speed.