Gibbs sampling

Gibbs sampling samples each variable conditioned on all others

Gibbs sampling is a Markov chain Monte Carlo (MCMC) algorithm used for sampling from complex multivariate distributions. It simplifies the sampling process by focusing on conditional distributions, making it practical for statistical inference tasks.

Gibbs sampling generates a sequence of samples that approximate the joint distribution of the variables. This method is particularly useful for Bayesian inference, where it helps to estimate unknown parameters or latent variables.

The algorithm is a randomized approach, providing an alternative to deterministic methods like the expectation–maximization algorithm (EM). It generates a Markov chain of samples, each correlated with the previous ones, allowing for efficient approximation of distributions.

Example

In a Bayesian network with variables A, B, and C, Gibbs sampling iteratively samples A given B and C, then B given A and C, and finally C given A and B.

Remember this

Understanding Gibbs sampling is crucial for effectively performing Bayesian inference and approximating complex distributions in statistical modeling.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

Related concepts

classifier-free guidance does: interpolates between conditional and unconditional generation

"Classifies samples as either conditioned or unconditioned, guiding generation towards desired outcomes."

Resampling (statistics)

Bootstrapping samples with replacement to estimate distributions

Langevin dynamics does: adds noise to gradient descent to sample from a distribution

Langevin dynamics uses stochastic differential equations

rejection sampling does: samples from target by accepting/rejecting proposals

Rejection sampling generates observations from a target distribution

importance sampling does: reweights samples from proposal to estimate target expectation

Importance sampling estimates target expectations using samples from a different distribution

Markov chain Monte Carlo

MCMC samples from complex posterior distributions

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