# About the Author

Hi! My Name is Dustin Stansbury. I recently received my PhD from UC Berkeley in Vision Science under the supervision of Jack Gallant. My academic research interests involve, but are not limited to:

- Neural Computation
- Machine Learning (particularly neural networks)
- Natural Scene Statistics
- Visual Perception
- Computer Vision
- Signal Processing
- Neuroimaging (e.g. Functional Magnetic Resonance Imaging (fMRI))

My personal/academic page is here.

Hi Dustin: Your explanation of MCMC using Hamiltonian dynamics is

the nicest, kindest, gentlest explanation that I have found and I have looked hard and was extremely confused until I read your explanation. I have to read it a few times for sure but I just have one question if you don’t mind. Could you explain how you get the original relations for partial x with respect to t and partial p with respect to t. You write both of them as a function of partial derivative of H and I don’t understand that step. Thank you very much for any enlightment and also for your beautiful hamiltonian explanation

.

Mark

Glad to be of help. As for the expressions dx/dt = dH/dp, and dp/dt = -dH/dx, those are simply the Hamilton’s characteristic equations. I didn’t come up with them, they are commonly used in physics to describe the dynamics of a closed system. Hamilton’s equations can be derived from the differential of the Langrangian for a closed system, but the derivation is somewhat involved. There is a nice example on Wikipedia, if you’re interested: http://en.wikipedia.org/wiki/Hamiltonian_mechanics

Hi, i really liked ur post on markov chains. However, i would also like to understand continuous time markov chains. If you can suggest any good help on its implementation in matlab it would be really great.

Your site is a fantastic resource — it’s good for me to remember that in addition to the vicious crap out there there is also treasure like this. Thanks so much for contributing to the signal.

Hi Dustin,

I would like to thank you and congratulate you about this amazing web. I think you are doing a very nice thing in here.

best

This is truly amazing work.