Comparative Analysis of EMCEE, Gaussian Process, and Masked Autoregressive Flow in Constraining the Hubble Constant Using Cosmic Chronometers Dataset

The Hubble constant ($H_0$) is essential for understanding the universe's evolution. Different methods, such as Affine Invariant Markov chain Monte Carlo Ensemble sampler (EMCEE), Gaussian Process (GP), and Masked Autoregressive Flow (MAF), are used to constrain $H_0$ using $H(z)$ data. However, these methods produce varying $H_0$ values when applied to the same dataset. To investigate these differences, we compare the methods based on their sensitivity to individual data points and their performance in constraining $H_0$. We apply Monte Carlo delete-$d$ jackknife (MCDJ) to assess their sensitivity to individual data points. Our findings reveal that GP is more sensitive to individual data points than both MAF and EMCEE, with MAF being more sensitive than EMCEE. Sensitivity also depends on redshift: EMCEE and GP are more sensitive to $H(z)$ at higher redshifts, while MAF is more sensitive at lower redshifts. In simulation-based performance tests, we generate an ensemble of mock CC datasets with a fixed input truth $H_{0,\mathrm{true}}$, apply each method to recover $H_0$ posteriors, and summarise performance by comparing the recovered posterior to $H_{0,\mathrm{true}}$: (i) posterior central value accuracy (bias and RMSE), (ii) credible-interval calibration (68\% and 95\% coverage), and (iii) overall posterior quality (log score), under two simulation prescriptions ($\Lambda$CDM-based and GP-based). Overall, EMCEE performs best, GP is intermediate, and MAF performs worst across the performance metrics.