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Target distribution
Probability distribution from which we wish to sample, often unknown or difficult to sample directly, requiring MCMC methods.
Proposal distribution
Distribution used to generate candidates in the Metropolis-Hastings algorithm, also called trial distribution or transition kernel.
Acceptance ratio
Probability of accepting a candidate in the Metropolis-Hastings algorithm, calculated as the minimum between 1 and the ratio of target densities multiplied by the ratio of proposal distributions.
Gibbs sampler
Special case of Metropolis-Hastings where proposals are always accepted, sampling conditionally each variable given the other variables.
Chain convergence
Moment when the Markov chain reaches its stationary distribution, crucial for ensuring the validity of samples generated by MCMC methods.
Random Walk Metropolis
Variant of Metropolis-Hastings where the proposal distribution is symmetric and centered on the current state, simplifying the calculation of the acceptance ratio.
Posterior
Probability distribution of parameters after observing data, obtained by Bayes' theorem and often sampled via MCMC.
Gelman-Rubin diagnostic
Diagnostic method evaluating the convergence of multiple MCMC chains by comparing within-chain variance to between-chain variance.
Trace plot
Graphique temporel montrant l'évolution des valeurs d'un paramètre à travers les itérations MCMC, utilisé pour évaluer visuellement la convergence et le mélange.
Detailed Balance
Condition mathématique garantissant que la distribution cible est la distribution stationnaire de la chaîne, essentielle pour la validité des algorithmes MCMC.
Rééchantillonnage importance
Technique associée aux MCMC pour corriger les poids des échantillons lorsque la distribution de proposition diffère significativement de la distribution cible.
Ergodicité
Propriété garantissant que les moyennes temporelles de la chaîne convergent vers les espérances sous la distribution stationnaire, fondamentale pour l'inférence MCMC.