这篇博客介绍了如何利用Gibbs Sampling进行多元高斯分布的采样，特别是在Bayesian inference中遇到的复杂分布问题。文章详细阐述了Gibbs Sampler的工作原理，并给出了在Python中实现的代码，通过10000次采样展示了从二元高斯分布中获取样本的过程。实验结果对比了实际分布和Gibbs Sampling的采样结果。
1. Introduction:
Gibbs Sampling is a MCMC method to draw samples from a potentially complicated, high dimensional distribution, where analytically, it’s hard to draw samples from it. The usual suspect would be those nasty integrals when computing the normalizing constant of the distribution, especially in Bayesian inference.
Gibbs Sampler can draw samples from any distribution, provided you have all of the conditional distributions of the joint distribution analytically.
2. Psudo-code:
3. Problem:
To use Gibbs Sampler to draw 10000 samples from a Bivariate Gaussian Distribution with
μ=[5,5],
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