Towards a model-independent reconstruction approach for late-time Hubble data

Abstract

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 -- 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. The kernel selection problem is not totally closed and may benefit from further analysis using other strategies to resolve an optimal kernel for a particular data set.