Fast and accurate calculations for cumulative first-passage time distributions in Wiener diffusion models

TY - JOUR

T1 - Fast and accurate calculations for cumulative first-passage time distributions in Wiener diffusion models

AU - Blurton, Steven Paul

AU - Kesselmeier, M.

AU - Gondan, Matthias

PY - 2012/12

Y1 - 2012/12

N2 - We propose an improved method for calculating the cumulative first-passage time distribution in Wiener diffusion models with two absorbing barriers. This distribution function is frequently used to describe responses and error probabilities in choice reaction time tasks. The present work extends related work on the density of first-passage times [Navarro, D.J., Fuss, I.G. (2009). Fast and accurate calculations for first-passage times in Wiener diffusion models. Journal of Mathematical Psychology, 53, 222-230]. Two representations exist for the distribution, both including infinite series. We derive upper bounds for the approximation error resulting from finite truncation of the series, and we determine the number of iterations required to limit the error below a pre-specified tolerance. For a given set of parameters, the representation can then be chosen which requires the least computational effort.

AB - We propose an improved method for calculating the cumulative first-passage time distribution in Wiener diffusion models with two absorbing barriers. This distribution function is frequently used to describe responses and error probabilities in choice reaction time tasks. The present work extends related work on the density of first-passage times [Navarro, D.J., Fuss, I.G. (2009). Fast and accurate calculations for first-passage times in Wiener diffusion models. Journal of Mathematical Psychology, 53, 222-230]. Two representations exist for the distribution, both including infinite series. We derive upper bounds for the approximation error resulting from finite truncation of the series, and we determine the number of iterations required to limit the error below a pre-specified tolerance. For a given set of parameters, the representation can then be chosen which requires the least computational effort.

UR - http://www.scopus.com/inward/record.url?scp=84875586839&partnerID=8YFLogxK

U2 - 10.1016/j.jmp.2012.09.002

DO - 10.1016/j.jmp.2012.09.002

M3 - Journal article

AN - SCOPUS:84875586839

SN - 0022-2496

VL - 56

SP - 470

EP - 475

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

IS - 6

ER -