Simulation Methods
This is a series of blog posts on simulation methods based on a statistics course called Advanced Simulation Methods (ASM) that I took in the University of Oxford between January and March 2014. The course was taught by Rémi Bardenet and Pierre Jacob. My understanding and appreciation of much of the content of the course only materialised when I wrote my dissertation supervised on Bayesian neural networks by Yee Whye Teh and my research project on exact Hamiltonian Monte Carlo with Louis Aslett.
Plan of Attack
- Introduction to Simulation Methods
- Classical Simulation Methods
- Importance Sampling
- Markov Chains
- Gibbs Sampler
- Metropolis Hastings
- Reversible Jump MCMC
- Sequential Importance Sampling
- Hidden Markov Models
- Stochastic Gradient MCMC
- Hamiltonian Monte Carlo
- Exact HMC
Each chapter comes with its own exercises and answers. I will be focusing more on computing and implementing the samplers rather than the mathematics. I will be using Clojure in the answers. Contributions for other languages are welcomed!
Creating the PDFs
Install Docker, and simply run the command ./run in the root directory of the repository.
Why Did I Decide To Write This?
Some courses are life-changing. This happened to be one of such courses for me. ASM made me work intensively on computational statistics, and looking back, it undoubtedly set the trajectory of my career and brought me to where I am today. Aside from emotional attachments, the course was good fun and extremely enriching. Therefore, I am making it a mission to share it with everyone!