SONIFICATION OF MARKOV CHAIN MONTE CARLO SIMULATIONS                                                            

T. Hermann                               M. H. Hansen                                H. Ritter                   
Faculty of Technology                       Bell Laboratories                   Faculty of Technology              
Bielefeld University, Germany                Murray Hill, New Jersey            Bielefeld University, Germany           
thermann@techfak.uni-bielefeld.de                cocteau@bell-labs.com            helge@techfak.uni-bielefeld.de            


ABSTRACT
Markov chain Monte Carlo (McMC) simulation is a popular computational 
tool for making inferences from complex, high-dimensional probability 
densities. Given a particular target densityp,
idea behind this technique is to simulate a Markov chain that has                                                            
pas 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 mon-                                                              
itoring, we have found our sonication 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 targpeta 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.                                                                     





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