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Chapter 12 describes diffusion models for continuous-outcome decision tasks, in which responses are expressed on continuous spatial scales. Many real-world, action-oriented decisions are of this kind and they are also important in laboratory studies of perception and memory. The chapter describes the circular diffusion model (CDM) of Smith and the spatially continuous diffusion model (SCDM) of Ratcliff and describes applications of the models to data. The CDM assumes that evidence is accumulated by a two-dimensional Wiener diffusion process with a vector-valued drift rate on the interior of a disk whose bounding circle represents the decision criterion. The SCDM assumes an infinite array of correlated accumulators with a Gaussian drift rate function. Evidence is accumulated on a line or the interior of a disk, depending on the geometry of the task. Fits of the models to the joint distributions of response times and accuracy are presented. Generalization of the CDM to higher dimensions leads to spherical and hyperspherical models, which can be handled using the same mathematical methods that are used to analyze the CDM. Applications of these higher-dimensional models are described.
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