gen-explain-bayesian-versus-frequentist-inference-as-you-would-t-c15a

Explain Bayesian versus frequentist inference as you would to a capable student, in 3-4 sentences.

# Bayesian vs Frequentist Inference **Frequentist inference** treats probability as long-run frequency: parameters have fixed (but unknown) true values, and we use data to estimate them or test hypotheses about them, quantifying uncertainty through concepts like confidence intervals and p-values. **Bayesian inference** treats probability as degree of belief: we start with prior beliefs about parameters, then update these beliefs using observed data via Bayes' theorem to get posterior distributions that directly quantify our uncertainty about parameter values. The key practical difference is that Bayesians can make direct probability statements about parameters ("there's a 95% probability the effect size is between 0.2 and 0.5"), while frequentists can only make statements about what would happen if we repeated the experiment many times ("95% of such intervals would contain the true value").