Bayesian Inference
Bayesian inference updates a prior distribution over parameters with data via Bayes’ rule to get a posterior — beliefs as probabilities, not just a point estimate.
Definition
p(θ|data) ∝ p(data|θ) p(θ). The posterior mean, median, or a full predictive distribution can be the decision object. Priors are not cheating; they are assumptions you can write down. Frequentist procedures hide them in the estimator.
Why it matters
Black–Litterman is Bayes on expected returns. Kalman filters are sequential Bayes. Calibration debates are prior debates.
Case
A PM with a strong prior that r* is 1% will not fully adopt a 3% nowcast. That is Bayes, not stubbornness — unless the prior never updates.
How to read it
Write the prior and the likelihood. If you cannot, you are not doing Bayes; you are adjective-ing.
Key papers
Landmark references with real publisher or arXiv links — not token-overlap noise.
- An Essay towards Solving a Problem in the Doctrine of ChancesBayes · 1763 · Philosophical TransactionsBayes’ rule.