MCMC Applets

Metropolis-Hastings algorithms are commonly used in Physics and Statistics for purposes of simulation and numerical integration, and these are often the only viable option when dealing with large scale problems in high dimensions.

The basic idea is to devise a Markov chain with a given equilibrium distribution, and then run it for as long as necessary while monitoring various functionals of interest.

I have written a few Java applets with demonstrations of some of the most common M-H algorithms.

To view these applets, you will need a Java 1.1 compatible navigator (either Netscape Navigator 4.06 or Internet Explorer 4.0 will do). If you have problems, see the section below entitled "Trouble running the applets".

The Applets

Metropolis-Hastings Algorithms is an applet which showcases many common Markov chain algorithms. Click on this link to view a short description of the featured algorithms. The applet itself will appear in a separate window.

Ever wondered what the transition matrix for the M-H algorithms above look like? Look no further, with M-H Roadmap.

Simulated Annealing is a mutation of the Metropolis-Hastings applet which shows how to use MCMC algorithms to find the global maxima of a given function.

Want more?

Check out Jeff Rosenthal's MCMC related applets (you may prefer to try his brand new soccer game). There's also Wilfrid Kendall's Dead Leaves Simulation, if you're in a morbid frame of mind :).

Trouble running the applets?

To run the applets, you need a web browser which is fully Java 1.1 compatible. If you don't have one, you can get the latest one now from either Netscape (download Netscape Navigator 4.06 or later) or Microsoft (download Internet Explorer 4.0 or later). Two problems (at least ;-) can occur.

You are running an old version of the web browser. If you are running Netscape, the programs should work fine with Netscape Navigator 4.06; if you have an older version and don't want to upgrade, you will need to download the Java 1.1 Patch. If you are running Microsoft, the programs should work fine under Internet Explorer 4.0 or later.
You have the correct web browser, but Java is disabled. If you are running Netscape, use the menu Edit|Preferences|Advanced and see if Java is enabled or not. It must be enabled for the applets to work.

Page maintained by Laird Breyer (email: L.Breyer@statslab.cam.ac.uk)