Title: Efficient Inference in First Passage Time Models Show Chinese title

Title: 首次通过时间模型中的高效推断

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. Show Chinese abstract

Abstract: 首先通过时间模型描述随机过程退出感兴趣区域所需的时间，并在各个科学领域中被广泛使用。 对于这些模型中似然函数的计算，快速且准确的数值方法对于高效的统计推断至关重要。 具体来说，在数学心理学中，广义漂移扩散模型（GDDMs）是一类重要的首先通过时间模型，用于描述简单决策场景背后的潜在心理过程。 GDDMs将选择和反应时间的联合分布建模为一维随机微分方程（SDE）首次击中可能随时间变化的上下边界的时间。 它们被广泛应用于提取与不同认知和神经机制相关的参数。 然而，当前的似然计算方法在处理每个试验中漂移率与外生协变量动态共变的常见场景时存在困难，例如在注意力漂移扩散模型（aDDM）中。 在这项工作中，我们提出了一种基于满足Cherkasov条件的大类SDE的GDDMs似然函数计算的快速且灵活的算法。 我们的方法将每个试验划分为离散阶段，利用快速解析结果计算阶段密度，并将其整合以计算整个试验的似然。 数值例子表明，我们的方法不仅能够为高效的统计推断提供准确的似然评估，而且在速度方面显著优于现有方法。