# Normalizing Constant Estimation with Gaussianized Bridge Sampling

arXiv: https://arxiv.org/abs/1912.06073 · HTML: https://mlsanity.com/paper/1912.06073/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2019.

## Built on by (most cited first, 6 of 6)

- [On Sampling with Approximate Transport Maps](https://mlsanity.com/paper/2302.04763/) (2023)
- [Improving Bridge estimators via f-GAN](https://mlsanity.com/paper/2106.07462/) (2021)
- [Active learning of Boltzmann samplers and potential energies with quantum mechanical accuracy](https://mlsanity.com/paper/2401.16487/) (2024)
- [NEO: Non Equilibrium Sampling on the Orbit of a Deterministic Transform](https://mlsanity.com/paper/2103.10943/) (2021)
- [Accelerated Bayesian parameter estimation and model selection for gravitational waves with normalizing flows](https://mlsanity.com/paper/2410.21076/) (2024)
- [BayesNDE: Bayesian Generative Modeling for Neural Density Estimation](https://mlsanity.com/paper/2609.39843/) (2026)

## Abstract (arXiv)

Normalizing constant (also called partition function, Bayesian evidence, or marginal likelihood) is one of the central goals of Bayesian inference, yet most of the existing methods are both expensive and inaccurate. Here we develop a new approach, starting from posterior samples obtained with a standard Markov Chain Monte Carlo (MCMC). We apply a novel Normalizing Flow (NF) approach to obtain an analytic density estimator from these samples, followed by Optimal Bridge Sampling (OBS) to obtain the normalizing constant. We compare our method which we call Gaussianized Bridge Sampling (GBS) to existing methods such as Nested Sampling (NS) and Annealed Importance Sampling (AIS) on several examples, showing our method is both significantly faster and substantially more accurate than these methods, and comes with a reliable error estimation.