MCMC Robot

An educational/teaching tool for demonstrating the basic principles of the Markov chain Monte Carlo (MCMC) method used for numerical integration of probability distributions. Allows user to create one or more bivariate normal "hills" in a two dimensional field and start one to four "robots" walking on this surface. The steps taken by each robot represent a single Markov chain, and large samples of steps illustrate how MCMC simulation can approximate a probability density surface. If the case of multiple robots, one represent the "cold" chain while the other "heated" chains illustrate improvements in mixing resulting from swapping of chains (Metropolis-coupled MCMC).

更新履歴
This app has been updated by Apple to display the Apple Watch app icon.

This version fixes problems resulting from the evolution of iOS, changes the behavior of the app when the device is rotated (orientation of hills now stays the same regardless of portrait or landscape orientation), and changes the way boundaries are enforced (the robots no longer bounce off boundaries, but instead steps proposed outside the boundaries are now simply rejected).