Three Samplers, One Posterior: NUTS vs. Emcee vs. Nested Sampling

Three Bayesian sampling methods—NUTS, emcee, and nested sampling (dynesty)—are benchmarked against problems with known ground-truth posteriors. While all three samplers handle simple, elliptical posteriors correctly, their performance diverges on more complex distributions. For a multimodal problem, NUTS gets stuck in local modes but its diagnostics clearly indicate failure. In contrast, emcee confidently provides incorrect results by misallocating probability across modes, with no clear warnings. Only nested sampling with dynesty successfully navigates the multimodal landscape to find the correct posterior distribution.