http://arxiv.org/abs/2106.08688
Gaussian processes offers a convenient way to perform nonparametric reconstructions of observational data assuming only a kernel which describes the covariance between neighbouring points in a data set. We approach the ambiguity in the choice of kernel in Gaussian processes with two methods — (a) approximate Bayesian computation with sequential Monte Carlo sampling and (b) genetic algorithm — in order to address the often ad hoc choice of the kernel and use the overall resulting method to reconstruct the cosmic chronometers and supernovae type Ia data sets. The results have shown that the Mat\'{e}rn$\left( \nu = 5/2 \right)$ kernel emerges on top of the two-hyperparameter family of kernels for both cosmological data sets. On the other hand, we use the genetic algorithm in order to select a most naturally-fit kernel among a competitive pool made up of a ten-hyperparameters class of kernels. Imposing a Bayesian information criterion-inspired measure of the fitness, the results have shown that a hybrid of the radial basis function and the Mat\'{e}rn$\left( \nu = 5/2 \right)$ kernel best represented both data sets.
R. Bernardo and J. Said
Thu, 17 Jun 21
24/74
Comments: 20 pages, 6 figures, 7 tables, comments welcome
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