PUB - Publikationen an der Universität Bielefeld

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.