To characterize the uncertainty in the DRT recovery, the posterior probability distribution p(x|Z exp ) (introduced in Section 2.1) was sampled using the No-U-Turn sampler (NUTS) algorithm. NUTS represents an efficient Markov Chain Monte Carlo algorithm based on Hamiltonian Monte Carlo chosen specifically for its effectiveness in sampling complex, high-dimensional posterior distributions. The algorithm enhances standard HMC by adaptively determining the trajectory length, avoiding inefficient "U-turns" in parameter space, thus improving sampling speed and exploration .