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

Видео The Metropolis Algorithm канала Drawing Distributions