The Metropolis Algorithm

The Metropolis algorithm is an incredibly important Markov chain Monte Carlo (MCMC) method. This statistical tool helps us sample from non-standard probability distributions. These distributions are hard to handle mathematically and arise from custom probabilistic models. In this video, you will build a solid understanding of the Metropolis algorithm by piecing it together from basic principles. Wondering what you'll learn? In this video, you'll explore: 1. What a Markov chain is: transition probabilities and stationary distributions 2. The components of the Metropolis algorithm: proposal distributions, acceptance probabilities, and detailed balance. 3. A step-by-step example of using the Metropolis algorithm to sample from the posterior distribution in a Bayesian image denoising task. 4. Convergence of MCMC samplers: transient and periodic Markov chains. This is the third episode in a multi-part series leading up to Hamiltonian Monte Carlo (HMC). Subscribe and join the journey as we lay the groundwork to master advanced MCMC techniques. Timestamps 0:00 Markov Chains: Typing 3:32 The proposal distribution 4:12 The acceptance probability 4:51 The stationary distribution 5:27 Detailed balance 6:38 The Metropolis algorithm 8:08 Image denoising example: Lily the Beagle 13:03 Convergence 14:57 What's next References/Further Reading 1. Bishop, C. M., & Nasrabadi, N. M. (2006). Pattern recognition and machine learning (Vol. 4, No. 4, p. 738). New York: springer. Chapter 8 2. MacKay, D. J. (2003). Information theory, inference and learning algorithms. Chapter 29 3. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (1995). Bayesian data analysis. Chapters 11 & 12 (third edition) #machinelearning #MCMC #drawingdistributions