Quantifying model uncertainty and performing model selection within a Bayesian framework is becoming an ever-larger part of scientific analysis both within and outside of astronomy. I will present a brief introduction to Nested Sampling, a complementary framework to Markov Chain Monte Carlo approaches that is designed to estimate marginal likelihoods (Bayesian evidences) and posterior distributions, outline some of its pros and cons, and briefly discuss more recent extensions such as Dynamic Nested Sampling.
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