Author:

Keywords:

Social Sciences, Psychology, Mathematical, Psychology, Experimental, Psychology, RESPONSE-TIMES, MODELS, Algorithms, Analysis of Variance, Computer Simulation, Humans, Models, Statistical, Monte Carlo Method, Probability, Stochastic Processes, 0801 Artificial Intelligence and Image Processing, 1701 Psychology, 1702 Cognitive Sciences, Experimental Psychology, 4905 Statistics, 5202 Biological psychology, 5204 Cognitive and computational psychology

Abstract:

Four methods for the simulation of the Wiener process with constant drift and variance are described. These four methods are (1) approximating the diffusion process by a random walk with very small time steps; (2) drawing directly from the joint density of responses and reaction time by means of a (possibly) repeated application of a rejection algorithm; (3) using a discrete approximation to the stochastic differential equation describing the diffusion process; and (4) a probability integral transform method approximating the inverse of the cumulative distribution function of the diffusion process. The four methods for simulating response probabilities and response times are compared on two criteria: simulation speed and accuracy of the simulation. It is concluded that the rejection-based and probability integral transform method perform best on both criteria, and that the stochastic differential approximation is worst. An important drawback of the rejection method is that it is applicable only to the Wiener process, whereas the probability integral transform method is more general.