  Nested sampling has emerged as a valuable tool for Bayesian analysis, in
particular for determining the Bayesian evidence. The method is based on a
specific type of random sampling of the likelihood function and prior volume of
the parameter space. I study the statistical uncertainty in the evidence
computed with nested sampling. I examine the uncertainty estimator from
Skilling (2004, 2006) and introduce a new estimator based on a detailed
analysis of the statistical properties of nested sampling. Both perform well in
test cases and make it possible to obtain the statistical uncertainty in the
evidence with no additional computational cost.
