During nuclear reactor operation, excessive hydrogen absorption in the cladding can lead to the formation of hydrides, significantly compromising cladding integrity. In this study, the Hydride Nucleation-Growth-Dissolution (HNGD) model, which accounts for the precipitation and dissolution kinetics of hydrides in Zircaloy, has been implemented using the COMSOL Multiphysics simulation platform. The sensitivity analysis conducted in this work identifies key parameters affecting hydrogen behavior in the fuel cladding and quantifies their impact on hydrogen distribution. This includes calculating first-order and total effect Sobol indices to measure the influence of individual parameters on the prediction of total hydrogen concentration under temperature gradients. Additionally, Bayesian inverse uncertainty quantification (IUQ) is applied to address the input uncertainties of critical model parameters. In the Bayesian framework, the model parameters are statistically calibrated under observation conditions by evaluating their joint posterior probability density function (PDF). This posterior PDF is inferred by sampling the parameters using the Markov Chain Monte Carlo (MCMC) algorithm. The resulting parametric uncertainty can serve as a robust substitute for expert opinion in future studies on uncertainty, sensitivity, and model validation.