Bayesian Estimation

Reference for Bayesian estimation in quantitative social science: from prior elicitation to MCMC implementation to posterior reporting. Covers the full workflow of specifying a Bayesian model, running inference, diagnosing convergence, and communicating results — with applications to structural models, hierarchical designs, and small-sample settings.

When to Use This Skill

Use when the user is:

• Specifying priors and setting up a Bayesian model in Stan, PyMC, NumPyro, brms, or rstanarm
• Running MCMC and diagnosing R-hat, ESS, divergences, or trace plots
• Implementing hierarchical (multilevel) models with partial pooling
• Adding Bayesian inference to a structural model (BLP, dynamic discrete choice, DSGE)
• Reporting credible intervals, posterior predictive checks, or model comparison statistics
• Eliciting priors from calibration targets or literature benchmarks
• Debugging sampling pathologies: divergences, low acceptance rates, poor mixing

Skip when:

• The model is large-N and well-identified (frequentist MLE/GMM is more efficient and faster)
• The task is pure structural estimation without Bayesian components (use structural-modeling skill)
• The user needs classical causal inference (use causal-inference skill)