Drift diffusion models (DDMs) have found widespread use in computational neuroscience, cognitive science, mathematical psychology as well as other fields. They model evidence accumulation in simple decision tasks as a stochastic process drifting towards decision barriers. In models where the drift is both time-varying within a trial and variable across trials, the high computational cost for accurate likelihood evaluation has often led to the use of a computationally convenient surrogate for parameter inference, the time-averaged drift approximation (TADA). In each trial, TADA assumes that the time-varying drift rate can be replaced by its temporal average throughout the trial. This approach enables fast parameter inference using analytical likelihood formulas for DDMs with constant drift. In this work, we show that such an estimator is inconsistent: it does not converge to the true drift, posing a risk of biasing scientific conclusions when parameter estimates are obtained by TADA and similar approximations. We provide an elementary proof of this inconsistency in what is perhaps the simplest possible setting: a Brownian motion with piecewise constant drift hitting a one-sided upper boundary. Furthermore, numerical examples based on an attentional DDM (aDDM) show that using TADA leads to systematic misestimation of attentional effects in decision making and can lead to false conclusions in scientific hypothesis testing.

翻译：扩散漂移模型在计算神经科学、认知科学、数理心理学及其他领域得到广泛应用。该模型将简单决策任务中的证据积累过程建模为向决策边界漂移的随机过程。当漂移量在单次试验内随时间变化，且在不同试验间存在差异时，精确似然计算的高昂计算成本常促使研究者采用一种计算便捷的参数推断替代方法——时间平均漂移近似。在每个试验中，时间平均漂移近似假设随时间变化的漂移率可由其在整个试验周期内的时域平均值替代。该方法通过恒定漂移扩散漂移模型的分析似然公式实现快速参数推断。本研究证明，此类估计量存在不一致性：其无法收敛至真实漂移参数，当通过时间平均漂移近似及类似近似方法获取参数估计时，可能导致科学结论产生偏差。我们在最简设定——即布朗运动以分段恒定漂移量击中单侧上界——中给出该不一致性的基础证明。此外，基于注意力扩散漂移模型的数值实例表明，采用时间平均漂移近似会导致决策过程中注意力效应的系统性误估，并在科学假设检验中引发错误结论。