Understand
Nested sampling is a promising tool for Bayesian statistical analysis because it simultaneously performs parameter estimation and facilitates model comparison.
- MultiNest is one of the most popular nested sampling implementations, and has been applied to a wide variety of problems in the physical sciences.
- However, MultiNest results, like those of any sampling tool, can be unreliable, and accompanying convergence tests are a necessary component of any analysis.
- Using analytically tractable test problems, I illustrate how MultiNest, when applied without rigorously chosen hyperparameters, (1) can produce systematically erroneous estimates of the Bayesian evidence, which are more significantly biased for problems of higher dimensionality; (2) can derive posterior estimates with errors on the order of $\sim100\%$; (3) can, particularly when sampling noisy likelihood functions, systematically underestimate posterior widths.