Nested Sampling for Uncertainty Quantification and Rare Event Estimation

Jonas Latz; Doris Schneider; Philipp Wacker

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arXiv · 2310.03040

Nested Sampling for Uncertainty Quantification and Rare Event Estimation

Jonas Latz·Doris Schneider·Philipp Wacker

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Abstract

Nested Sampling is a method for computing the Bayesian evidence, also called the marginal likelihood, which is the integral of the likelihood with respect to the prior. More generally, it is a numerical probabilistic quadrature rule. The main idea of Nested Sampling is to replace a high-dimensional likelihood integral over parameter space with an integral over the unit line by employing a push-forward with respect to a suitable transformation. Practically, a set of active samples ascends the level sets of the integrand function, with the measure contraction of the super-level sets being statistically estimated. We justify the validity of this approach for integrands with non-negligible plateaus, and demonstrate Nested Sampling's practical effectiveness in estimating the (log-)probability of rare events.

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Jonas Latz, Doris Schneider, Philipp Wacker. 2023-10-02. Nested Sampling for Uncertainty Quantification and Rare Event Estimation. https://arxiv.org/abs/2310.03040

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