  Nested sampling is widely used in astrophysics for reliably inferring model
parameters and comparing models within a Bayesian framework. To address models
with many parameters, Markov Chain Monte Carlo (MCMC) random walks are
incorporated within nested sampling to advance a live point population.
Diagnostic tools for nested sampling are crucial to ensure the reliability of
astrophysical conclusions. We develop a diagnostic to identify problematic
random walks that fail to meet the requirements of nested sampling. The
distance from the start to the end of the random walk, the jump distance, is
divided by the typical neighbor distance between live points, computed robustly
with the MLFriends algorithm, to obtain a relative jump distance (RJD). We
propose the geometric mean RJD and the fraction of RJD>1 as new summary
diagnostics. Relative jump distances are investigated with mock and real-world
inference applications, including inferring the distance to gravitational wave
event GW170817. Problematic nested sampling runs are identified based on
significant differences to reruns with much longer MCMC chains. These
consistently exhibit low average RJDs and f(RJD>1) values below 50 percent. The
RJD is more sensitive than previous tests based on the live point insertion
order. The RJD diagnostic is proposed as a widely applicable diagnostic to
verify inference with nested sampling. It is implemented in the UltraNest
package in version 4.1.
