🤖 AI Summary
Efficient likelihood computation remains challenging for generalized drift-diffusion models (GDDMs) when the drift rate varies dynamically with time-varying covariates (e.g., neural activity, visual fixation). To address this, we propose a staged, analytically driven fast inference algorithm. Our method extends the Cherkasov condition to GDDMs with time-varying boundaries and integrates stochastic differential equation analytical solutions, piecewise density propagation, and adaptive numerical integration to achieve high-precision likelihood estimation. Evaluated on canonical tasks—including the attentional drift-diffusion model (aDDM)—our approach matches Monte Carlo “gold-standard” accuracy while accelerating computation by one to two orders of magnitude. This work establishes the first likelihood computation framework for dynamic-covariate-coupled decision models that simultaneously ensures analytical tractability, computational efficiency, and broad applicability across GDDM variants.
📝 Abstract
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. Specifically, in mathematical psychology, 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 with common scenarios where drift rates covary dynamically with exogenous covariates in each trial, such as in the attentional drift diffusion model (aDDM). 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 significantly outperforms existing approaches in terms of speed.