Gibbs Sampling

This article introduces the combination of Bayesian methods and Markov Random Fields (MRF) through an image segmentation example. By introducing ‘Homogeneity Prior’ and ‘Gibbs Sampling’, it demonstrates how to use MRF to solve image denoising and segmentation problems, and compares the results of traditional Maximum Likelihood, MRF Simulated Annealing, and the Simple Relaxation (ICM) method commonly used in industry. [Read More]

When high-dimensional spaces are overwhelming, Gibbs sampling adopts a ‘divide and conquer’ strategy. By utilizing full conditional distributions, it breaks down complex N-dimensional joint sampling into N simple 1-dimensional sampling steps. This article explains its intuition, mathematical proof (Brook’s Lemma), and Python implementation. [Read More]