Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic, regardless of the reference time scale. Thus, we propose to augment mechanistic cognitive models with a temporal dimension and estimate the resulting dynamics from a superstatistics perspective. In its simplest form, such a model entails a hierarchy between a low-level observation model and a high-level transition model. The observation model describes the local behavior of a system, and the transition model specifies how the parameters of the observation model evolve over time. To overcome the estimation challenges resulting from the complexity of superstatistical models, we develop and validate a simulation-based deep learning method for Bayesian inference, which can recover both time-varying and time-invariant parameters. We first benchmark our method against two existing frameworks capable of estimating time-varying parameters. We then apply our method to fit a dynamic version of the diffusion decision model to long time series of human response times data. Our results show that the deep learning approach is very efficient in capturing the temporal dynamics of the model. Furthermore, we show that the erroneous assumption of static or homogeneous parameters will hide important temporal information.
翻译:认知的数学模型往往没有记忆,忽视其参数的潜在波动。然而,人类认知是内在动态的,不管参考时间尺度如何。因此,我们提议增加具有时间尺度的机械化认知模型,并从超统计角度估计由此产生的动态。以最简单的形式,这种模型涉及低水平观测模型和高层次过渡模型之间的等级分级。观察模型描述一个系统的当地行为,而过渡模型则具体说明观察模型的参数如何随时间演变。为了克服超统计模型的复杂性所产生的估计挑战,我们制定并验证一种基于模拟的贝叶斯推论深学习方法,该方法既可以恢复时间变化参数,也可以恢复时间变化参数。我们首先根据两个现有框架确定我们的方法,能够估计时间变化参数。然后,我们运用我们的方法将一个动态的传播决定模型的动态版本与长期的人类响应时间序列数据相匹配。我们的研究结果表明,深度学习方法将非常高效地捕捉该模型的时空动态。此外,我们展示了错误的定时参数假设。