# Testing the Drift-Diffusion Model

## TL;DR

This paper introduces a statistical test for the drift-diffusion model (DDM), enabling validation and estimation of its parameters in binary decision tasks, with applications across psychology and neuroscience.

## Contribution

It provides a characterization theorem for DDM choice probabilities, ensuring their identification and enabling nonparametric estimation of drift and boundary functions.

## Key findings

- Characterization theorem for DDM choice probabilities
- Unique identification of drift and boundary parameters
- Nonparametric estimation and testing procedure for DDM

## Abstract

The drift diffusion model (DDM) is a model of sequential sampling with diffusion (Brownian) signals, where the decision maker accumulates evidence until the process hits a stopping boundary, and then stops and chooses the alternative that corresponds to that boundary. This model has been widely used in psychology, neuroeconomics, and neuroscience to explain the observed patterns of choice and response times in a range of binary choice decision problems. This paper provides a statistical test for DDM's with general boundaries. We first prove a characterization theorem: we find a condition on choice probabilities that is satisfied if and only if the choice probabilities are generated by some DDM. Moreover, we show that the drift and the boundary are uniquely identified. We then use our condition to nonparametrically estimate the drift and the boundary and construct a test statistic.