Bayesian inference for psychology, part IV: parameter estimation and Bayes factors

Area of Science:

• Psychology
• Statistics
• Statistical Inference

Background:

• Two primary inference methods exist in psychology: posterior interval estimation and Bayes factors.
• These methods appear distinct but share common ground through specific model choices.

Purpose of the Study:

• To unify the approaches of posterior interval estimation and Bayes factors.
• To demonstrate how spike-and-slab priors bridge these two inferential techniques.
• To highlight the role of model specification in statistical inference.

Main Methods:

• Overview of posterior interval estimation and Bayes factor approaches.
• Introduction of spike-and-slab priors as a unifying model specification.
• Analysis of effect size estimation as a function of Bayes factors.

Main Results:

• Posterior interval estimation and Bayes factors can be unified using spike-and-slab priors.
• Effect size estimation is shown to be a function of the Bayes factor.
• A key difference lies in whether the null hypothesis is privileged, impacting analytical goals.

Conclusions:

• Spike-and-slab priors offer a unified framework for estimation and model comparison.
• The choice between privileging the null hypothesis or not depends on the analyst's specific research objectives.
• Both estimation and Bayes factor approaches are valuable tools in statistical analysis.