The optimization process is carried out subject to constraints, such as for example design parameter ranges and/or cost constraints. This is generally a numerically complex and computationally expensive procedure. It typically requires to explore the design parameters space (e.g., via MCMC), generating at each point a set of pseudo-data that are analysed as real data would, in order to compute their FoM. Then the search algorithm moves on to maximize the FoM.
In order to carry out the optimization procedure, it might be useful to adopt a principal component analysis (PCA) to determine a suitable parametrization of [468, 838]. The redshift range of the survey can be split into bins, with the equation of state taking on a value in the -th bin:
One can now reconstruct by keeping only a certain number of the most accurately determined modes, i.e., the ones with largest eigenvalues. The optimal number of modes to retain can be estimated by minimizing the risk, defined as the sum of the bias squared (how much the reconstructed equation of state departs from the true one by neglecting the more noisy modes) plus the variance of the estimate .
Living Rev. Relativity 16, (2013), 6
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