The canonical computational model for the cognitive process underlying two-alternative forced-choice decision making is the so-called drift–diffusion model (DDM). In this model, a decision variable keeps track of the integrated difference in sensory evidence for two competing alternatives. Here I extend the notion of a drift–diffusion process to multiple alternatives. The competition between n alternatives takes place in a linear subspace of $n-1$ dimensions; that is, there are $n-1$ decision variables, which are coupled through correlated noise sources. I derive the multiple-alternative DDM starting from a system of coupled, linear firing rate equations. I also show that a Bayesian sequential probability ratio test for multiple alternatives is, in fact, equivalent to these same linear DDMs, but with time-varying thresholds. If the original neuronal system is nonlinear, one can once again derive a model describing a lower-dimensional diffusion process. The dynamics of the nonlinear DDM can be recast as the motion of a particle on a potential, the general form of which is given analytically for an arbitrary number of alternatives.

中文翻译：

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用于多选强制选择决策的漂移扩散模型。

两种备选强制选择决策基础上的认知过程的规范计算模型是所谓的漂移扩散模型（DDM）。在此模型中，决策变量会跟踪两种竞争选择的感官证据的综合差异。在这里，我将漂移扩散过程的概念扩展为多种选择。n个替代方案之间的竞争发生在$ n-1 $维的线性子空间中；也就是说，有$ n-1 $个决策变量，它们通过相关的噪声源耦合。我从耦合线性点火速率方程式的系统中推导了多种替代DDM。我还表明，针对多种选择的贝叶斯顺序概率比检验实际上等效于这些相同的线性DDM，但具有随时间变化的阈值。如果原始神经元系统是非线性的，则可以再次导出描述低维扩散过程的模型。可以将非线性DDM的动力学重塑为粒子在电势上的运动，其一般形式通过任意数量的替代方法进行分析给出。