Inference of cosmological models with principal component analysis

Determination of cosmological parameters is a major goal in cosmology at present. The availability of improved data sets necessitates the development of novel statistical tools to interpret the inference from a cosmological model. In this paper, we combine the principal component analysis (PCA) and Markov Chain Monte Carlo (MCMC) method to infer the parameters of cosmological models. We use the No U-Turn Sampler (NUTS) to run the MCMC chains in the model parameter space. After determining the observable by PCA, we replace the observational and error parts of the likelihood analysis with the PCA reconstructed observable and find the most preferred model parameter set. To demonstrate our methodology, we assume a polynomial expansion as the parametrization of the dark energy equation of state and plug it into the reconstruction algorithm as our model. After testing our methodology with simulated data, we apply the same to the observed data sets, the Hubble parameter data, Supernova Type Ia data, and the Baryon acoustic oscillation data. This method effectively constrains cosmological parameters from data, including sparse data sets.