Gibbs Sampling é uma Cadeia de Markov Monte Carlo (MCMC) algorithm used for obtaining a sequence of samples from a distribuição de probabilidade conjunta when direct sampling is difficult. This technique is particularly useful in high-dimensional spaces where traditional sampling methods may fail.
The core idea behind Gibbs Sampling is to iteratively sample from the conditional distributions of each variable, given the current values of all the other variables. For instance, in a scenario with two variables, X and Y, the algorithm would first sample a value for X from its conditional distribution P(X|Y), then update Y by sampling from P(Y|X), and repeat this process. This results in a sequence of samples that converge to the target distribuição conjunta.
One of the key advantages of Gibbs Sampling is its simplicity and ease of implementation, especially when the conditional distributions are easy to sample from. It is widely used in various fields such as estatísticas bayesianas, machine learning, and image processing. However, Gibbs Sampling can have slow convergence rates, particularly if the variables are highly correlated.
Na prática, as primeiras amostras geradas pela Amostragem de Gibbs muitas vezes são descartadas (um processo conhecido como burn-in) para permitir que a cadeia converja para a distribuição alvo. As amostras restantes podem então ser usadas para estimar propriedades da distribuição, como médias, variâncias e outras estatísticas.