Sonification of the Hybrid Monte Carlo Algorithm

• Activity Number: 257
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing*
• Author(s): Matthias Heymann*+
• Affiliation(s): Bell Labs, Lucent Technologies
• Keywords: Sonification ; Hybrid monte carlo ; Markov chain Monte Carlo

Abstract

The hybrid Monte Carlo algorithm combines the Metropolis sampler with a deterministic step based on Newtonian mechanics. Graphical methods are often used to assess characteristics of the sampler. These methods become difficult in high-dimensional cases. To address this problem, I develop a new tool that is based on sound rather than graphics. I regard the negative density function of the distribution as a potential function. Every sample is then used as the starting point of a ball that moves according to this potential, and its kinetic energy as a function over time is audified. The character and the frequency of the sound depend on the starting position of the ball. I then sonify every sample belonging to the sequence of samples from the algorithm.

As a first result for a two-dimensional test distribution, one can hear clearly if the number of steps between two samples is chosen too small, since the character of the tones changes only slowly.

A new package for R that contains 35 commands to deal with sound samples was developed and can be used easily by everybody who wants to try his own ideas of sonification.

For examples see www.MatthiasHeymann.de/mathematics.html