Learned harmonic mean estimation of the Bayesian evidence with normalizing flows
arxiv(2024)
摘要
We present the learned harmonic mean estimator with normalizing flows - a
robust, scalable and flexible estimator of the Bayesian evidence for model
comparison. Since the estimator is agnostic to sampling strategy and simply
requires posterior samples, it can be applied to compute the evidence using any
Markov chain Monte Carlo (MCMC) sampling technique, including saved down MCMC
chains, or any variational inference approach. The learned harmonic mean
estimator was recently introduced, where machine learning techniques were
developed to learn a suitable internal importance sampling target distribution
to solve the issue of exploding variance of the original harmonic mean
estimator. In this article we present the use of normalizing flows as the
internal machine learning technique within the learned harmonic mean estimator.
Normalizing flows can be elegantly coupled with the learned harmonic mean to
provide an approach that is more robust, flexible and scalable than the machine
learning models considered previously. We perform a series of numerical
experiments, applying our method to benchmark problems and to a cosmological
example in up to 21 dimensions. We find the learned harmonic mean estimator is
in agreement with ground truth values and nested sampling estimates. The
open-source harmonic Python package implementing the learned harmonic mean, now
with normalizing flows included, is publicly available.
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