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MCMC (Markov Chain Monte Carlo)
Class of sampling algorithms that build a Markov chain with the posterior distribution as its stationary distribution to perform approximate inference in complex graphical models.
Metropolis-Hastings algorithm
General MCMC algorithm that uses a proposal distribution to generate new states and accepts/rejects these proposals according to a probability criterion ensuring convergence to the target distribution.
Burn-in
Initial MCMC sampling period during which samples are discarded because the chain has not yet reached its stationary distribution, eliminating the influence of the initial state.
Mixing time
Number of iterations required for a Markov chain to get sufficiently close to its stationary distribution, measuring the speed of convergence of MCMC algorithms.
Rejection sampling
Direct sampling technique that generates candidates from an envelope distribution and accepts them with a probability proportional to the ratio of the target/envelope densities.
Importance sampling
Monte Carlo method using importance weights to correct the bias introduced by sampling from a proposal distribution different from the target distribution.
Sequential Monte Carlo
Set of algorithms (particle filters) for inference in sequential models, using sets of weighted particles to approximate sequential distributions.
Hamiltonian Monte Carlo
Advanced MCMC variant that uses Hamiltonian mechanics to propose distant states with high acceptance probability, reducing the autocorrelation of the samples.
Gelman-Rubin Diagnostic
Statistical method for assessing the convergence of MCMC chains by comparing within-chain and between-chain variance, with a value close to 1 indicating convergence.
Thinning
Technique involving keeping only a subset of MCMC samples to reduce autocorrelation and storage, typically by keeping every k-th sample.
Approximate Evidence Inference
Methods for estimating the marginal likelihood (evidence) in graphical models, essential for model selection and Bayesian computation.
Slice Sampling
MCMC technique that introduces auxiliary variables to simplify sampling from complex distributions, particularly useful for multimodal distributions.
Blackwell-MacQueen Variant
Sequential sampling algorithm for Dirichlet processes, generating samples according to the Blackwell-MacQueen predictive distribution.
Antithetic Sampling
Variance reduction technique using negatively correlated sample pairs to improve the efficiency of Monte Carlo estimation.