Hello everyone, we will talk about the topic Hybrid MC, more specifically the Random Walk, Langevin MC and Hamiltonian MC.

First we will make a short introduction by talking about our target and challenges, and we will review the Metropolis-Hastings Algorithm shortly, which we have learned in the course. After that we will talk about Random Walk and MALA which is metropolis adjusted langevin algorithm. Then comes the core role of our presentation Hamiltonian MC. Besides we will also show our experiment result of these three algorithms and compare them.

Let's get started.

First, our final target of using all these algorithm is to compute the expectation of fx on a distribution. We learned from the course that the expectation can be written as integral, the expectation of f on pi is f q pi q integrated on the sample space big Q. Here dq is kind of a volume