  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. As a
demonstration of our methodology, we assume a polynomial expansion as the
parametrization of the dark energy equation of state and plug it in 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.
