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A General Approach to Prior Transformation.

Simon Segert¹, Clintin P Davis-Stober²

¹Princeton University.

Journal of Mathematical Psychology

|August 25, 2020

Summary

This summary is machine-generated.

Researchers can now set prior distributions in Bayesian models using a general method for re-parameterized parameters. This Bayesian approach offers improved tools for cognitive and decision-making models, enhancing statistical analysis.

Keywords:

Bayes Factors Bayesian Priors Cognitive Models Inference

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Area of Science:

Cognitive Science
Decision Science
Bayesian Statistics

Background:

Bayesian models are widely used in cognitive and decision-making research.
Setting appropriate prior distributions is crucial for robust Bayesian inference.
Existing methods for prior specification can be limited, especially with re-parameterized models.

Purpose of the Study:

To present a general method for setting prior distributions in Bayesian models with re-parameterized parameters.
To generalize existing work by accommodating differing parameter space dimensions.
To provide numerical methods for models lacking closed-form solutions.

Main Methods:

Development of a general framework for prior specification in Bayesian models.
Generalization of Heck and Wagenmakers (2016) to unequal parameter space dimensions.
Application of numerical methods for prior specification in complex models.
Reanalysis of data from the Selective Integration model using the proposed methods.

Main Results:

The proposed method facilitates prior specification for a broader range of Bayesian models.
Bayes factor analysis indicated that the four-parameter Selective Integration model outperformed simpler variants and a competitor model.
This contrasts with previous findings using BIC, highlighting the sensitivity of model comparison to the chosen metric.

Conclusions:

The developed methods offer a more complete toolkit for researchers specifying priors in Bayesian cognitive and decision-making models.
The Selective Integration model is better supported with all four parameters when analyzed with Bayes factors.
The study provides both theoretical advancements and practical tools for Bayesian data analysis.