- Thomas Hermann, Mark H. Hansen, Helge Ritter (2001)
In Hiipakka, Jarmo and Zacharov, N. and Takala, Tapio (Ed.) Proceedings of 7th International Conference on Auditory Display, p. 208--216, ICAD, Laboratory of Acoustics and Audio Signal Processing and the Telecommunications Software and Multimedia Laboratory, Helsinki University of Technology
[BibTeX Entry]
Summary
Markov chain Monte Carlo (McMC) simulation is a popular computational tool for making inferences from complex, high-dimensional probability densities. Given a particular target density , the idea behind this technique is to simulate a Markov chain that has as its stationary distribution. To be successful, the chain needs to be run long enough so that the distribution of the current draw is close to the target density. Unfortunately, very few diagnostic tools exist to monitor characteristics of the chain. In this paper, we present a new approach to render sonifications of McMC simulations. The proposed method consists of several auditory streams which provide information about the behavior of the Markov chain. In particular, we focus on uncovering modes in the target density function. In addition to monitoring, we have found our sonification to be an effective means for understanding the structure of high-dimensional densities. We have also applied our method to the exploratory analysis of high-dimensional data sets. In this case, we take as our target a non-parametric density estimate obtained from the data. In this paper, we present a detailed description of our sonification design and illustrate its performance on test cases consisting of both synthetic and real-world data sets. Sound examples are also given.
- Example E0: Using audification of particle trajectories (section 3.3 in the paper).
- Example E1: Audification of particle trajectories started at McMC steps (section 5.1 in the paper).
- (a) The Audification of 100 McMC steps in a distribution p with 3 modes
- (b) This example is rendered for a data set in 6d data space with 3 clusters. To give an impression how these audifications may sound like we give 3 examples, differing in nr. of steps (N), time between steps (TimePerStep) and friction coefficient (gamma)
- Soundfile (a): T = ##, N = ##, gamma = ## -- WAVE-file MP3-file
- Soundfile (b): T = ##, N = ##, gamma = ## -- WAVE-file MP3-file
- Soundfile (c): T = ##, N = ##, gamma = ## -- WAVE-file MP3-file
- Example E2: Using McMC process stream, AIB stream and McMC details stream as introduced in the paper
- (a) dataset: 3 clusters in 6 dimensional space. T = 0.01
- McMC stream: WAVE-file MP3-file
- McMC details stream: WAVE-file MP3-file
- AIB stream: WAVE-file MP3-file
- All streams together: WAVE-file MP3-file
- (b) dataset: 3 clusters in 6 dimensional space. T = 0.002
- McMC stream: WAVE-file MP3-file
- McMC details stream: WAVE-file MP3-file
- AIB stream: WAVE-file MP3-file
- All streams together: WAVE-file MP3-file
- (c) dataset: 6 clusters in 6 dimensional space, T = 0.008
- McMC stream: WAVE-file MP3-file
- McMC details stream: WAVE-file MP3-file
- AIB stream: WAVE-file MP3-file
- All streams together: WAVE-file MP3-file
- (d) dataset: 3 clusters in 6 dim. space, T = 0.002, p computed by kernel density estimation but now with a kernel of bandwidth sigma such that p is unimodal.
- Example E3: Sonification of McMC simulations for handwritten digits (section 5.3 in the paper)
- Example E4: Sonification of McMC simulations for Bayesian Models (section 5.4 in the paper)
- Example E5: Sonification of McMC simulation on iris dataset
Contact
Thomas Hermann
Helge Ritter
Sonification of Markov-chain Monte Carlo Simulations
Media files
Listen to a single particle converging to a mode in a three-modal density function p. This example corresponds to figure 2 in the paper. Files: WAVE-file.
Listen to a similar particle with an increased friction coefficient
of 0.9996. On each step, the kinetic energy is reduced to E(t+1) = 0.9996
E(t), resulting in an exponential decay of energy. Sounds: WAVE-file
Soundfile: WAVE-File
This examples are discussed in the paper in section 5.2.
This examples are discussed in the paper in section 5.5.
The following examples are sonification with
bandwidth scaling exponent | soundfile |
0.5 | WAVE-file MP3-file |
0.25 | WAVE-file MP3-file |
0 | WAVE-file MP3-file |
-0.25 | WAVE-file MP3-file |
-0.5 | WAVE-file MP3-file |
-0.75 | WAVE-file MP3-file |
-1 | WAVE-file MP3-file |