Even faster and even more accurate first-passage time densities and distributions for the Wiener diffusion model
نویسندگان
چکیده
TheWiener diffusion model with two absorbing barriers is often used to describe response times and error probabilities in two-choice decisions. Different representations exist for the density and cumulative distribution of first-passage times, all including infinite series, but with different convergence for small and large times. We present a method that controls the approximation error of the small-time representation that occurs due to finite truncation of these series. Our approach improves and simplifies related work by Navarro and Fuss (2009) and Blurton et al. (2012, both in the Journal of Mathematical Psychology). © 2014 Elsevier Inc. All rights reserved.
منابع مشابه
Fast and accurate calculations for first-passage times in Wiener diffusion models
We propose a new method for quickly calculating the probability density function for first passage times in simple Wiener diffusion models, extending an earlier method used by Van Zandt, Colonius and Proctor (2000). The method relies on the observation that there are two distinct infinite series expansions of this probability density, one of which converges quickly for small time values, while ...
متن کاملThe first - passage time distribution for the diffusion model with variable drift
23 The Ratcliff diffusion model is now arguably the most widely applied model for response time 24 data. Its major advantage is its description of both response times and the probabilities for 25 correct as well as incorrect responses. The model assumes a Wiener process with drift between 26 two constant absorbing barriers. The first-passage times at the upper and lower boundary 27 describe the...
متن کاملGenerating Random Variables from the Inverse Gaussian and First-Passage-Two-Barrier Distributions
We investigate a naive method for generating pseudo-random variables from two distributions, the inverse Gaussian and the First-PassageTwo-Barrier distribution. These are the first passage time distributions of a Wiener process with non-zero drift to one and two barriers respectively. The method consists of simulating a path (a realization of the Wiener process) by constructing a step function ...
متن کاملروش بالادست چندبعدی براساس مشخصهها برای تحلیل جریان تراکم ناپذیر داخل حفره
In this research, a new multidimensional characteristic based upwind scheme for the solution of incompressible Navier-Stokes equations is presented. The incompressible flow equations have been coupled each other by the aid of artificial compressibility method. Unlike to the traditional characteristic based (CB) schemes, the present scheme is genuinely multidimensional in that the local charact...
متن کاملA martingale analysis of first passage times of time-dependent Wiener diffusion models.
Research in psychology and neuroscience has successfully modeled decision making as a process of noisy evidence accumulation to a decision bound. While there are several variants and implementations of this idea, the majority of these models make use of a noisy accumulation between two absorbing boundaries. A common assumption of these models is that decision parameters, e.g., the rate of accum...
متن کامل