Bayesian hierarchical models and prior elicitation for fitting psychometric functions.

Area of Science:

• Psychophysics
• Bayesian statistics
• Hierarchical modeling

Background:

• Generalized linear mixed models (GLMM) and two-level methods were previously used for psychophysical data analysis.
• Bayesian models offer advantages in reducing parameter uncertainty by integrating prior knowledge with experimental data.

Purpose of the Study:

• To revisit hierarchical models within a Bayesian framework for psychophysical data analysis.
• To evaluate uncertainties between and within participants using posterior distributions.
• To demonstrate the application of Bayesian models by re-analyzing tactile discrimination of speed data.

Main Methods:

• Utilized Bayesian hierarchical models for psychometric function analysis.
• Incorporated prior knowledge from literature and previous experiments into prior distributions.
• Employed a power prior distribution to modulate prior influence when fitting new datasets.
• Implemented models using Just Another Gibbs Sampler (JAGS) interfaced with R (rjags package).

Main Results:

• Bayesian models estimated probability distributions for parameters, providing insights into experimental variable effects and uncertainty.
• Quantified uncertainties both between and within individual participants.
• Demonstrated the utility of Bayesian approaches for analyzing psychometric functions in psychophysical experiments.

Conclusions:

• Bayesian hierarchical models provide a powerful method for analyzing psychometric functions.
• This approach effectively estimates parameter uncertainties and individual participant reliability.
• The integration of prior knowledge enhances the precision of parameter estimates in psychophysical research.