cs401r_w2016:lab10
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| For each different proposal distribution, you should run your MCMC chain for 10,000 steps, and record the sequence of states. Then, you should produce a visualization of the distribution of states, and overlay a plot of the actual target distribution. They may or may not match (see, for example, the first example plot in the Description section). | For each different proposal distribution, you should run your MCMC chain for 10,000 steps, and record the sequence of states. Then, you should produce a visualization of the distribution of states, and overlay a plot of the actual target distribution. They may or may not match (see, for example, the first example plot in the Description section). | ||
| - | Furthermore, for each proposal distribution, you should run three independent chains (you can do these sequentially or in parallel, as you like). You should display each of these three chains on a single plot with time on the x-axis and the state on the y-axis. Ideally, you will see each of the three chains mixing between two modes. | + | Furthermore, for each proposal distribution, you should run three independent chains (you can do these sequentially or in parallel, as you like). You should display each of these three chains on a single plot with time on the x-axis and the state on the y-axis. Ideally, you will see each of the three chains mixing between two modes; you may notice other features of the behavior of the samplers as well, which you should report in your writeup! |
| **Part 2: Hamiltonian MCMC** | **Part 2: Hamiltonian MCMC** | ||
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| A detailed explanation of Hamiltonian MCMC can be found here:[[http://www.mcmchandbook.net/HandbookChapter5.pdf|Hamiltonian MCMC]]. | A detailed explanation of Hamiltonian MCMC can be found here:[[http://www.mcmchandbook.net/HandbookChapter5.pdf|Hamiltonian MCMC]]. | ||
| - | - You will find the equations describing the leapfrog method in Equations 5.18, 5.19 and 5.20. | + | * You will find the equations describing the leapfrog method in Equations 5.18, 5.19 and 5.20. |
| - | - You will find a description of how to convert a given ''p(x)'' into a Hamiltonian in Section 5.3.1. | + | * You will find a description of how to convert a given ''p(x)'' into a Hamiltonian in Section 5.3.1. |
| - | - You will find a description of the complete HMC algorithm in section 5.3.2.1 | + | * You will find a description of the complete HMC algorithm in section 5.3.2.1 |
| - | Remember that you will alternate between two steps: | + | Remember that you will alternate between two steps: |
| + | |||
| + | - Sampling the momentum conditioned on the position. This is just sampling from a Gaussian. | ||
| + | - Proposing a new state for the position, given the momentum. This involves integrating the dynamics, and then accepting or rejecting based on integration error. | ||
| You will have to tune two parameters in order to implement HMC: the variance of the momentum variables, and the timestep used for integrating the dynamics. Experiment with both, and report your results using plots like those you prepared for Part 1. | You will have to tune two parameters in order to implement HMC: the variance of the momentum variables, and the timestep used for integrating the dynamics. Experiment with both, and report your results using plots like those you prepared for Part 1. | ||
cs401r_w2016/lab10.txt · Last modified: 2021/06/30 23:42 (external edit)
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