Confidence intervals vs. Credible intervals
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In the frequentist approach, the parameter θ is treated as an unknown fixed constant, and the data is treated as random. In the Bayesian approach, we treat the data as fixed (since it is known) and the parameter as random (since it is unknown). Probalistic Machine Learning
- Bayesian vs. Frequentist
- credible intervals are Bayesian and incorporate prior information
- confidence intervals are frequentist and rely solely on the observed data
- Interpretation
- credible intervals provide a direct probability statement about the parameter given the data and prior
- confidence intervals provide a range that would capture the true parameter value in repeated sampling
- Construction:
- credible intervals are derived from the posterior distribution
- confidence intervals are derived from the sampling distribution of the estimator