The seminal Nelson and Siegel (1987) model and its extensions are widely used by market participants such as central banks and portfolio managers as a yield curve model. This model is often calibrated with ordinary least squares (OLS) methods and, more recently, exploring heuristic-based methods such as differential evolution and genetic algorithms. In this chapter, we provide a first-in-literature exploration of the use of Hamiltonian Monte Carlo, the Separable Shadow Hybrid Hamiltonian Monte Carlo, and the No-U-Turn Sampler to calibrate the parameters of this model to simulated data, South African yield curve market data as well as a time series of USA corporate bond yield curve market data. This Bayesian framework provides a better understanding of the parameter distribution of the Nelson and Siegel (1987) model and includes uncertainty in yield curve estimations. Our analysis reveals that our calibration technique gives comparable or better yield curve estimates than OLS across various performance metrics while accounting for parameter uncertainty.