Fast and accurate calculations for first-passage times in Wiener diffusion models
By D. Navarro, Ian G. Fuss. 2009
183 citations recorded by the source corpus.
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, T., Colonius, H., & Proctor, R. W. (2000). A comparison of two response-time models applied to perceptual matching. Psychonomic Bulletin & Review, 7, 208–256]. 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 the other converges quickly at large time values. By deriving error bounds associated with finite truncation of either expansion, we are able to determine analytically which of the two versions should be applied in any particular context. The bounds indicate that, even for extremely stringent error tolerances, no more than 8 terms are required to calculate the probability density. By making the calculation of this distribution tractable, the goal is to allow more complex extensions of Wiener diffusion models to be developed.
Subfields: Cognitive Neuroscience
View Paper: https://www.semanticscholar.org/paper/14b34129e44ca7aa5ddaa7df67f8228e5e2419fa
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In Cognitive Neuroscience
- Thomas V. Wiecki
- Michael J Frank
- Imri Sofer
- Joachim Vandekerckhove
- Matthew Botvinick
- Randall C. O’Reilly
- A. G. Collins
- Peter S. Dayan
Citations in the corpus
- HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python (2013, methodology): “05 ) sv , st , sz ) where x i , j represents the observed data consisting of response time and choice of subject i on trial j and F represents the DDM likelihood function as formulated by Navarro and Fuss (2009).”
- A cognitive latent variable model for the simultaneous analysis of behavioral and personality data. (2014, methodology): “(1) Fortunately, efficient methods for the computation of the Wiener diffusion model density and distribution functions exist (Blurton, Kesselmeier, & Gondan, 2012; Navarro & Fuss, 2009, for the CDF and PDF, respectively), making it a highly tractable model.”