Figure 9 :
9(a) Sequences of 400 walkers from the kombine sampler over 150 iterations. Two randomly selected sequences are highlighted in black. All samples to the left of the black dashed line are discarded. (b) The marginal Likelihoods and 2-sigma standard deviations are plotted for both samplers and all models.Finally, we examine the Posterior distribution and uncertainty intervals.Figure 10summarizes the posterior distributions obtained via the kombine (left) and MultiNest (right) samplers. We plot histograms and KDE distributions for each univariate parameter distribution. We provide multivariate summaries for each pair of coefficients via scatter plots of 2000 randomly selected samples. True parameter values are indicated by black markers. We first note that the samplers produce similar posterior parameter distributions. Furthermore, regions of high density in the Posterior closely align with the true parameter values. Figure 11 displays the model prediction and 95 th percentile uncertainty intervals obtained via the kombine (left) and MultiNest (right) samplers versus the synthetic **data** points. The uncertainty intervals are obtained by randomly sampling the Posterior distributions of the model parameters and computing the 2.5 th and 97.5 th percentile levels of the resulting model predictions. The uncertainty intervals show the expected spread of model predictions from the distribution of θ 0 and θ 1 . The models fit the synthetic **data** well, and both the model predictions and uncertainty intervals are nearly indistinguishable between the two samplers. The results of
