Abstract
We present a new, fast approach for drawing boundary crossing samples from Wiener diffusion models. Diffusion models are widely applied to model choices and reaction times in two-choice decisions. Samples from these models can be used to simulate the choices and reaction times they predict. These samples, in turn, can be utilized to adjust the models’ parameters to match observed behavior from humans and other animals. Usually, such samples are drawn by simulating a stochastic differential equation in discrete time steps, which is slow and leads to biases in the reaction time estimates. Our method, instead, facilitates known expressions for first-passage time densities, which results in unbiased, exact samples and a hundred to thousand-fold speed increase in typical situations. In its most basic form it is restricted to diffusion models with symmetric boundaries and non-leaky accumulation, but our approach can be extended to also handle asymmetric boundaries or to approximate leaky accumulation.
Highlights
For a wide range of problems, human and animal decision-makers are known to trade-off the accuracy of choices with the speed with which these choices are performed
In its simplest form, a diffusion model is formed by a particle whose trajectory follows a stochastic Wiener process with overlayed deterministic drift until one of two boundaries is reached (Fig. 1(a))
The stochastic diffusion causes these times and choices to vary across different particle trajectory realizations
Summary
Fast approach for drawing boundary crossing samples from Wiener diffusion models. It does not suffer from any biases, as it directly draws exact samples by rejection sampling from the series expansion of the first-passage time density It is in the order of a hundred to a thousand times faster than simulating the whole particle trajectory with typical step-sizes. The sampling method only applies to diffusion models with symmetric boundaries around a central particle starting point, and a drift and diffusion variance that remains constant over time. It is embedded in simulations in which these parameters vary across trials.
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