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This paper introduces a novel hierarchical Bayesian model specificallydesigned to address challenges in Inverse Uncertainty Quantification (IUQ) fortime-dependent problems in nuclear Thermal Hydraulics (TH) systems. The uniquecharacteristics of time-dependent data, such as high dimensionality andcorrelation in model outputs requires special attention in the IUQ process. Byintegrating Gaussian Processes (GP) with Principal Component Analysis (PCA), weefficiently construct surrogate models that effectively handle the complexityof dynamic TH systems. Additionally, we incorporate Neural Network (NN) modelsfor time series regression, enhancing the computational accuracy andfacilitating derivative calculations for efficient posterior sampling using theHamiltonian Monte Carlo Method - No U-Turn Sampler (NUTS).  We demonstrate the effectiveness of this hierarchical Bayesian approach usingthe transient experiments in the PSBT benchmark. Our results show improvedestimates of Physical Model Parameters' posterior distributions and a reducedtendency for over-fitting, compared to conventional single-level Bayesianmodels. This approach offers a promising framework for extending IUQ to morecomplex, time-dependent problems.

Hierarchical Bayesian Modeling for Time-Dependent Inverse Uncertainty Quantification