Credible interval

A credible interval contains a specified proportion of a parameter’s posterior probability distribution, conditional on observed data and a statistical model. Its probability statement is Bayesian and depends on the model and prior.

Bayesian inference: Statistical inference that updates prior probabilities using observed data through Bayes’ theorem. A credible interval summarizes uncertainty after Bayesian updating.
Confidence interval: An interval procedure whose repeated-sampling coverage reaches a specified rate under its assumptions. Unlike a credible interval, its coverage statement concerns repeated samples, not posterior probability for fixed bounds.
Bayesian linear regression: Linear regression that assigns probability distributions to model parameters and updates them using data. Intervals summarize posterior uncertainty in its regression coefficients.
Parameterization: The choice of variables or coordinates used to represent a mathematical model or parameter space. A highest-density interval can change under nonlinear reparameterization.
Posterior distribution: A probability distribution for unknown quantities conditional on observed data and a statistical model. The interval’s stated probability is measured under this distribution.
Frequentist inference: Statistical inference that evaluates procedures by their behavior over repeated sampling. Its treatment of unknown parameters differs from the posterior-probability interpretation here.
Bayesian logistic regression: Logistic regression fitted using probability distributions for parameters and Bayesian updating. Its coefficient intervals quantify posterior uncertainty on the log-odds scale.
Prior sensitivity analysis: An assessment of how Bayesian conclusions change under plausible alternative prior distributions. A credible interval may shift or widen when prior assumptions change.
Prior probability: A probability distribution representing uncertainty about unknown quantities before incorporating the current data. The prior helps shape the posterior from which the interval is calculated.
Prediction interval: An interval intended to contain a future observation with a specified probability or coverage rate. It concerns a future data point rather than an unknown parameter’s posterior distribution.

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