This article is part of the Research Topic Python in Neuroscience II


Front. Neuroinform., 02 August 2013 |

HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python

  • Department of Cognitive, Linguistic and Psychological Sciences, Brown University, Providence, RI, USA

The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ2-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at:

Keywords: Bayesian modeling, drift diffusion model, Python, decision-making, software

Citation: Wiecki TV, Sofer I and Frank MJ (2013) HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python. Front. Neuroinform. 7:14. doi: 10.3389/fninf.2013.00014

Received: 07 May 2013; Paper pending published: 28 May 2013;
Accepted: 15 July 2013; Published online: 02 August 2013.

Edited by:

Yaroslav O. Halchenko, Dartmouth College, USA

Reviewed by:

Michael Hanke, Otto-von-Guericke-University, Germany
Eric-Jan Wagenmakers, University of Amsterdam, Netherlands
Dylan D. Wagner, Dartmouth College, USA

Copyright © 2013 Wiecki, Sofer and Frank. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Thomas V. Wiecki, Department of Cognitive, Linguistic and Psychological Sciences, Brown University, 190 Thayer St., Providence, RI 02912-1821, USA e-mail:

These authors have contributed equally to this work.