gen-briefly-explain-bayesian-versus-frequentist-inference-and-on-324f

Briefly explain Bayesian versus frequentist inference and one common misconception about it.

# Bayesian vs Frequentist Inference **Frequentist inference** treats probability as long-run frequency. Parameters are fixed but unknown, and we use data to construct procedures (like confidence intervals) that would perform correctly over many hypothetical repetitions of the experiment. **Bayesian inference** treats probability as degree of belief. Parameters are treated as random variables with distributions, and we update our prior beliefs about parameters using data (via Bayes' theorem) to get posterior distributions. ## Common Misconception **The misconception**: "A 95% confidence interval means there's a 95% probability the true parameter lies within it." **The reality**: In frequentist terms, a 95% CI means that if we repeated the sampling procedure many times, 95% of the constructed intervals would contain the true parameter. For any *specific* interval you've calculated, the parameter either is or isn't in it—there's no probability involved. The statement "95% probability the parameter is in this interval" is actually the *Bayesian* interpretation of a credible interval, not a frequentist confidence interval. This is perhaps the most common mix-up between the two frameworks.