Caballero Javier A, Lepora Nathan F, Gurney Kevin N
Dept of Psychology, University of Sheffield, Sheffield, UK; Faculty of Life Sciences, University of Manchester, Manchester, UK.
Dept of Engineering Mathematics, University of Bristol, Bristol, UK; Bristol Robotics Laboratory, University of Bristol and University of the West of England, Bristol, UK.
PLoS One. 2015 Apr 29;10(4):e0124787. doi: 10.1371/journal.pone.0124787. eCollection 2015.
Computational theories of decision making in the brain usually assume that sensory 'evidence' is accumulated supporting a number of hypotheses, and that the first accumulator to reach threshold triggers a decision in favour of its associated hypothesis. However, the evidence is often assumed to occur as a continuous process whose origins are somewhat abstract, with no direct link to the neural signals - action potentials or 'spikes' - that must ultimately form the substrate for decision making in the brain. Here we introduce a new variant of the well-known multi-hypothesis sequential probability ratio test (MSPRT) for decision making whose evidence observations consist of the basic unit of neural signalling - the inter-spike interval (ISI) - and which is based on a new form of the likelihood function. We dub this mechanism s-MSPRT and show its precise form for a range of realistic ISI distributions with positive support. In this way we show that, at the level of spikes, the refractory period may actually facilitate shorter decision times, and that the mechanism is robust against poor choice of the hypothesized data distribution. We show that s-MSPRT performance is related to the Kullback-Leibler divergence (KLD) or information gain between ISI distributions, through which we are able to link neural signalling to psychophysical observation at the behavioural level. Thus, we find the mean information needed for a decision is constant, thereby offering an account of Hick's law (relating decision time to the number of choices). Further, the mean decision time of s-MSPRT shows a power law dependence on the KLD offering an account of Piéron's law (relating reaction time to stimulus intensity). These results show the foundations for a research programme in which spike train analysis can be made the basis for predictions about behavior in multi-alternative choice tasks.
大脑决策的计算理论通常假定，感觉“证据”会不断积累以支持多个假设，并且第一个达到阈值的累加器会触发有利于其相关假设的决策。然而，人们常常认为证据是以连续过程的形式出现的，其起源有些抽象，与神经信号——动作电位或“尖峰”——没有直接联系，而神经信号最终必定构成大脑决策的基础。在此，我们引入了一种著名的多假设序贯概率比检验（MSPRT）的新变体用于决策，其证据观测由神经信号传导的基本单位——峰峰间隔（ISI）组成，并且基于一种新形式的似然函数。我们将这种机制称为s - MSPRT，并展示了它在一系列具有正支持的现实ISI分布下的精确形式。通过这种方式，我们表明，在尖峰层面，不应期实际上可能有助于缩短决策时间，并且该机制对于假设数据分布的不良选择具有鲁棒性。我们表明s - MSPRT的性能与ISI分布之间的库尔贝克 - 莱布勒散度（KLD）或信息增益相关，通过它我们能够在行为层面将神经信号传导与心理物理学观测联系起来。因此，我们发现决策所需的平均信息量是恒定的，从而为希克定律（将决策时间与选择数量联系起来）提供了一种解释。此外，s - MSPRT的平均决策时间显示出对KLD的幂律依赖性，为皮埃龙定律（将反应时间与刺激强度联系起来）提供了一种解释。这些结果为一个研究项目奠定了基础，在该项目中，尖峰序列分析可以作为预测多选项选择任务中行为的基础。
