Bayesian estimation
Update explicit assumptions into posterior uncertainty
Bayesian estimation combines a prior distribution with a likelihood to produce a posterior distribution over unknown quantities. Credible intervals and posterior predictions summarise model-conditional uncertainty. Priors can regularise estimates and encode relevant information, but require explanation and sensitivity analysis. Estimation differs from Bayes-factor model comparison, which addresses a different question.
Use when probabilistic parameter statements, hierarchical pooling or prior information suit the research question. Specify a defensible generative model and allocate time to prior checks, computation and sensitivity analysis.
Strengths
- Provides coherent joint uncertainty and predictions
- Allows regularisation and partial pooling
Limitations
- Results can be sensitive to priors and likelihood choices
- Complex models require careful computation and diagnostics
Know the boundary
A credible interval is conditional on the model; Bayesian analysis does not rescue an uninformative or biased design.