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# Wageningen methods used in gravitational wave analysis

It was headline news earlier this year: gravitational waves exist! In analysing them some hundred years after Einstein’s theoretical prediction, scientists used data processing techniques created by Cajo ter Braak, a scientist at Wageningen University & Research. The so-called Differential Evolution Markov Chain (DE-MC) Monte Carlo method was developed ten years ago for applications in modern research in the fields of agriculture, food and the environment. In the LIGO (Laser Interferometer Gravitational Wave Observatory) experiment the Wageningen discovery helped calculate a collision between two black holes some 1.3 billion years ago.

## Detecting gravitational waves

In the general theory of relativity by Einstein, the gravitational force exerted by mass is replaced by a curvature of space. If something happens to the mass, one can see this from a distance as a result of a change in the curvature of space, resulting in a temporary change in the length of a measuring rod along which the wave moves. The problem is that the effect is extremely small and an extreme event is required to observe the ripple with even the best available detection methods.

## Noise and complexity

The collision of two black holes, each with a mass which a few dozen times that of the sun, is quite extreme, and the LIGO experiment that can detect a change in length of ten to the power minus 18 metres (one thousandth of the diameter of an atomic nucleus) on a measuring rod of one kilometre is one of the best detection methods available. But that’s not enough. Two other problems that must be overcome are noise and complexity. A good data processing method is needed for the latter, which is where the Wageningen DE-MC method comes in.

Every experiment, no matter how accurate, suffers from noise. What seems like a signal can be caused by something else than what the scientist is trying to detect; from a passing caterpillar to a power interruption as a result of the northern lights. Moreover, the intended signal is generated by a complex process: how exactly do the black holes rotate around each other before colliding? This complexity makes it difficult to establish the values of the parameters of the process from the noisy signal. This is exactly what the DE-MC method was developed for and why it is universally applicable.

## A great match

Thirteen parameters were used to describe the collision. A well-known statement, attributed to one of the great mathematicians of our time, John von Neumann, states: ‘with four parameters I can fit an elephant, and with five I can make him wiggle his trunk’. Continuing this line of thought, it is a small miracle that 13 parameters do not result in total chaos. The essence of the method is to play with the parameter values in a clever way, instead of becoming hopelessly lost in the high dimensional parameter space. The clever jumps of DE-MC in the parameter space help describe the minuscule ripples in actual space, making it, in hindsight, a match made in heaven!