Figure displays parameter values and their uncertainties determined using MC explorations compared to the Cramér-Rao lower bounds on the parameters given by ARM+LSQ. The orange curves were generated using Gaussian components having positions and integrated amplitudes coming from the ARM+LSQ fits. Widths of the components are the marginalized standard deviations of the rates from the Cramér-Rao bounds given by the inverse Fisher information matrices. The blue curves are determined from binning the MC calculations. Amplitudes of the components for each step are added in the bin corresponding to the relaxation rate sampled by the algorithm. For both types of curves, the total amplitude was normalized to unity prior to plotting. Using three-components as suggested by ARM+LSQ using component selection heuristics, the components appear mono-modal in both types of display. For this example, the MC method found slightly different maximum likelihood values compared to ARM+LSQ, though that is not always the case. Monte Carlo also finds higher uncertainties compared to the Cramér-Rao lower bound. This is not surprising if the response of 2  to parameter variations is slightly non-parabolic. For the four- component case, MC methods find several different parameter combinations that are similarly likely to account for the data. Standard deviations from the Cramér-Rao lower-bound do not accommodate this behavior because of the underlying assumption of a locally parabolic 2  surface. For the five-component case, the covariances of the parameters lead to Cramér-Rao lower-bound uncertainties that are very large relative to the differences in the optimized relaxation rates. This is supported by broad but jagged distributions from MC. Inspection of the parameter value trajectories from MC (not shown) indicate that the parameter values do not settle into well-defined ranges, but instead appear to be diffusing in a very large parameter space. This indicates that only a small region of the available likely parameter space is explored by the algorithm in the allotted number of steps (25,000).