  Nested sampling (NS) computes parameter posterior distributions and makes
Bayesian model comparison computationally feasible. Its strengths are the
unsupervised navigation of complex, potentially multi-modal posteriors until a
well-defined termination point. A systematic literature review of nested
sampling algorithms and variants is presented. We focus on complete algorithms,
including solutions to likelihood-restricted prior sampling. A new formulation
of NS is presented, which casts the parameter space exploration as a search on
a tree. Previously published ways of obtaining robust error estimates and
dynamic variations of the number of live points are presented as special cases
of this formulation.
