Bayesian Regression Analysis & Posterior Inference

I will conduct a Bayesian regression analysis using Stan (via brms in R) or PyMC — covering prior specification with justification, posterior sampling with MCMC diagnostics, posterior distribution interpretation with credible intervals, Bayesian model comparison (LOO-CV), and a results report presenting Bayesian conclusions correctly to an audience familiar with frequentist reporting. Bayesian regression provides richer inference than frequentist approaches — posterior distributions, probability that an effect exceeds a threshold, and direct probability statements about parameters — but requires careful prior specification and MCMC diagnostic checking that frequentist software does not demand.

The analysis covers prior specification with sensitivity analysis, MCMC sampling with convergence diagnostics (R-hat, effective sample size, trace plots), posterior predictive check, coefficient posterior summary with credible intervals, probability of direction and ROPE analysis, LOO-CV model comparison, and a results write-up explaining posterior findings clearly.

Designed for researchers and analysts who want Bayesian inference for its interpretational advantages, for small-sample research where frequentist power is insufficient, or for methodologically sophisticated audiences requiring full posterior uncertainty quantification.