General constrained randomisation

  Randomisation schemes based on the Fourier amplitudes of the data are appropriate in many cases. However, there remain some flaws, the strongest being the severely restricted class of testable null hypotheses. The periodogram estimator of the power spectrum is about the only interesting observable that allows for the solution of the inverse problem of generating random sequences under the condition of its given value.

In the general approach of Ref. [26], constraints (e.g. autocorrelations) on the surrogate data are implemented by a cost function which has a global minimum when the constraints are fulfilled. This general framework is much more flexible than the Fourier based methods. We will therefor discuss it in some detail.

 
• Null hypotheses, constraints, and cost functions
• Computational issues of simulated annealing
• Example: avoiding periodicity artefacts
• Combinatorial minimisation and accuracy
• The curse of accuracy