Mathematics

Learn about Markov processes, stationary distributions, and convergence of Markov chains. [Read More]

Understand the core concepts of Monte Carlo: Law of Large Numbers, rejection sampling, importance sampling, variance reduction techniques (antithetic variates, control variates, stratified sampling). [Read More]

The reason we need MCMC is that many distributions are only known in their unnormalized form, making traditional sampling/integration methods ineffective. By constructing a ‘correct Markov chain’, we can obtain the target distribution from its stationary distribution, meaning the long-term distribution of the trajectory ≈ target distribution. [Read More]

This article introduces the basic concepts and rigorous formulas of probability, serving as the foundation for understanding random variables, sampling, and MCMC. [Read More]