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Bayesian Calibration
Calibration method using Bayesian inference to estimate model parameters by incorporating prior knowledge and observed data, quantifying uncertainty.
Likelihood Function
Function measuring the probability of observing the data given specific model parameter values, essential for Bayesian inference.
Markov Chain Monte Carlo (MCMC)
Class of sampling algorithms that generate samples from complex distributions to approximate posterior distributions in Bayesian calibration.
Credible Interval
Probability interval containing a specified proportion of a parameter's posterior distribution, the Bayesian equivalent of a confidence interval.
Hierarchical Bayesian Model
Bayesian model structure with multiple levels of parameters where hyperparameters govern the distributions of lower-level parameters.
Posterior Predictive Distribution
Distribution of future predictions that incorporates parameter uncertainty by weighting predictions by the posterior distribution.
Conjugate Prior
Prior distribution chosen to belong to the same family as the posterior distribution, mathematically simplifying Bayesian inference.
Bayes Factor
Ratio of marginal likelihoods that allows quantitative comparison of different Bayesian models for selection and validation.
Hamiltonian Monte Carlo
Advanced MCMC algorithm using Hamiltonian mechanics to efficiently explore the parameter space in complex Bayesian models.
Posterior Predictive Check
Diagnostic validation method comparing observed data to simulated predictions from the posterior distribution to assess model adequacy.
Bayesian Model Averaging
Approach combining predictions from multiple models weighted by their posterior probabilities to reduce model uncertainty.
Prior Predictive Distribution
Distribution of predictions based solely on the prior distributions of parameters, used to verify the coherence of initial knowledge.