An adaptive rejection sampler for sampling from the Wiener diffusion model

Area of Science:

• Psychological research methodology
• Computational modeling
• Statistical analysis

Background:

• The Wiener diffusion model is widely used for analyzing response times and accuracy in cognitive tasks.
• Existing sampling methods may be slow, especially with complex model parameters like variable drift rate, starting point, and non-decision time.

Purpose of the Study:

• To evaluate and compare four sampling methods for the Wiener diffusion model.
• To introduce and assess two novel adaptive rejection sampling (ARS) techniques.
• To provide practical guidelines for selecting efficient sampling methods.

Main Methods:

• Implementation of inverse transform sampling, rejection sampling, and two ARS-based methods in an R package.
• Validation of sampling methods to ensure accurate distribution generation.
• Comparative analysis of sampling speed across different settings and sample sizes.

Main Results:

• All four implemented sampling methods successfully generated samples from the intended distributions.
• Adaptive rejection sampling (ARS) methods demonstrated superior sampling speed, particularly as the required sample size increased.
• The efficiency of ARS versus traditional methods depends on specific model parameters and sample size.

Conclusions:

• Adaptive rejection sampling (ARS) offers a more efficient approach for sampling from the Wiener diffusion model, especially for large datasets.
• The study provides valuable insights for researchers on optimizing computational efficiency in diffusion model analysis.
• The developed R package facilitates the application of these advanced sampling techniques in psychological research.