Bayesian inference is the general method of learning from data by starting with a prior belief and revising it after seeing evidence.
The pieces
Bayesian inference works with four core parts:
- a prior for what was believed before the data,
- a likelihood for how probable the observed data are under different hypotheses,
- a posterior after updating,
- and often a predictive distribution for future observations.
The update follows Bayes theorem:
$$ \text{Posterior} \propto \text{Likelihood} \times \text{Prior} $$
Economic relevance
Economists use Bayesian inference when agents or researchers must revise beliefs about uncertain quantities such as inflation persistence, growth trends, default probabilities, or the effect of a policy.
It also mirrors how many economic models describe learning: people do not restart from zero every period, they update from what they already believed.
Bayesian vs. frequentist framing
The Bayesian question is usually, “given the data, how plausible is each parameter value or hypothesis?” That differs from the classical frequentist emphasis on sampling distributions and repeated-sample properties.
Both approaches are useful. Bayesian inference is especially attractive when prior information is economically meaningful or when the researcher wants direct probability statements about parameters.