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Bayesian inference with Stan: A tutorial on adding custom distributions.

Jeffrey Annis¹, Brent J Miller², Thomas J Palmeri²

¹Vanderbilt University, 111 21st Ave S., 301 Wilson Hall, Nashville, TN, 37240, USA. jeff.annis@vanderbilt.edu.

Behavior Research Methods

|June 12, 2016

Summary

This summary is machine-generated.

Bayesian approaches offer superior parameter estimation for cognitive models compared to traditional methods. The Stan software package efficiently handles complex models and custom distributions, improving Bayesian inference.

Keywords:

Bayesian inference Linear ballistic accumulator Probabilistic programming Stan

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Area of Science:

Cognitive Science
Computational Neuroscience
Statistical Modeling

Background:

Parameter estimation is crucial for evaluating cognitive models.
Traditional methods yield point estimates, lacking uncertainty quantification.
Existing Bayesian software (WinBUGS, JAGS) can be inefficient for correlated parameters and difficult for custom distributions.

Purpose of the Study:

Introduce Stan as a solution for efficient Bayesian inference in cognitive modeling.
Provide a tutorial on using Stan and implementing custom distributions.
Demonstrate Stan's utility with the linear ballistic accumulator model.

Main Methods:

Utilized Stan, a probabilistic programming language and platform.
Developed custom distributions within Stan for cognitive models.
Applied Stan to the linear ballistic accumulator model for parameter estimation.

Main Results:

Stan effectively addresses inefficiencies with correlated parameters.
Stan simplifies the addition of custom distributions for cognitive models.
The tutorial demonstrates a practical application of Stan in cognitive modeling.

Conclusions:

Stan offers a powerful and flexible tool for Bayesian cognitive modeling.
Stan enhances parameter estimation and model comparison in cognitive science.
The presented tutorial facilitates the adoption of Stan for researchers.