June 12, 2004

a drunk mans walk through the CMB

Being of an occasional nosey disposition I chanced to glance at a paper some of my "colleagues" were discussing over a cup of tea, "Fast and reliable MCMC for cosmological parameter estimation". My attention was grabbed by the word "markov" (MCMC = markov chain monte carlo). Here was something I knew something about, I thought. In my understanding a markov chain is a way to proceed along some path according to various probabilities. Arriving at any node in the path the chain specifies the probabilities of moving to each of a number of other nodes. In this way a network emerges which can be navigated in many different ways according to these probabilities at each node, at each point where a choice need be made.

They (Joanna Dunkley, Martin Bucher, Pedro G. Ferreira, Kavilan Moodley and Constantinos Skordis) were using markov chains to make cosmological parameter estimations. Taking a combination of various parameters including baryon density, dark matter density and the age of the universe, they were using the markov technique to determine which values of these parameters best fits the CMB (Cosmic Microwave Background) data. (CMB : see numerous previous posts).

Roughly speaking the technique involves taking a point and comparing it to the previous point. If the new point is higher, probability wise, then you move to this point. If it's lower, whether one moves is dependant on how much lower it's probability is. In this way one zig zags around the space of possible solutions closing in on the best fit, the highest probability.

This graph plots one such path.

It occured to me that this might be interesting to listen to. Jo Dunkley gave me lists of 1000 values generated by the markov chains and I scaled them up to audible frequencies. The list was iterated through, playing sine tones with these frequencies.

Base note b flat an octave below middle c :

Transposed up 20 semitones :

The data expressed logarithmically :

They sound pretty good together too . . . (they should play in seperate windows).

Posted by Jem Finer at June 12, 2004 5:59 PM