15 minute talk given on 21st October 2020 at the 3rd global 21cm workshop

Nested sampling is an alternative Markov-chain Monte-Carlo technique for integrating and exploring probability distributions. With publicly available implementations such as MultiNest, PolyChord and dynesty, nested sampling has become widely adopted in astronomy as a powerful tool for computing Bayesian evidences and sampling challenging a-priori unknown parameter spaces. In this talk I will give a user's guide to the theory of nested sampling in the context of 21cm Bayesian model comparison and parameter estimation, a survey of the current state of the art and the future of the field. This will aim to provide theoretical background for the Bayesian inference techniques and algorithms underpinning the science of several other talks which focus on applying nested sampling to 21cm cosmology.

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