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Analyzing dynamic decision-making models using Chapman-Kolmogorov equations.
Journal of Computational Neuroscience ( IF 1.2 ) Pub Date : 2019-11-16 , DOI: 10.1007/s10827-019-00733-5
Nicholas W Barendregt 1 , Krešimir Josić 2 , Zachary P Kilpatrick 1
Affiliation  

Decision-making in dynamic environments typically requires adaptive evidence accumulation that weights new evidence more heavily than old observations. Recent experimental studies of dynamic decision tasks require subjects to make decisions for which the correct choice switches stochastically throughout a single trial. In such cases, an ideal observer’s belief is described by an evolution equation that is doubly stochastic, reflecting stochasticity in the both observations and environmental changes. In these contexts, we show that the probability density of the belief can be represented using differential Chapman-Kolmogorov equations, allowing efficient computation of ensemble statistics. This allows us to reliably compare normative models to near-normative approximations using, as model performance metrics, decision response accuracy and Kullback-Leibler divergence of the belief distributions. Such belief distributions could be obtained empirically from subjects by asking them to report their decision confidence. We also study how response accuracy is affected by additional internal noise, showing optimality requires longer integration timescales as more noise is added. Lastly, we demonstrate that our method can be applied to tasks in which evidence arrives in a discrete, pulsatile fashion, rather than continuously.

中文翻译:

使用Chapman-Kolmogorov方程分析动态决策模型。

在动态环境中进行决策通常需要自适应证据的积累,而新证据的权重要比旧观测值高。动态决策任务的最新实验研究要求受试者做出决策,在单个试验中,正确选择会随机切换。在这种情况下,理想的观察者的信念是由双随机的演化方程描述的,反映了观测值和环境变化的随机性。在这些情况下,我们表明可以使用差分Chapman-Kolmogorov方程表示信念的概率密度,从而可以高效地计算整体统计量。这使我们能够可靠地将规范模型与近似规范近似值进行比较,方法是将模型性能指标用作标准 决策分布的决策响应准确性和Kullback-Leibler散度。可以通过要求受试者报告他们的决策信心来从经验中获得这种信念分布。我们还研究了附加内部噪声如何影响响​​应精度,这表明随着添加更多噪声,最优性需要更长的积分时间范围。最后,我们证明了我们的方法可用于以离散,易动而不是连续的方式到达证据的任务。
更新日期:2019-11-16
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