Bayesian Posterior Repartitioning for Nested Sampling

@article{Chen2022BayesianPR,
  title={Bayesian Posterior Repartitioning for Nested Sampling},
  author={Xi Chen and Farhan Feroz and Michael P. Hobson},
  journal={Bayesian Analysis},
  year={2022}
}
. Priors in Bayesian analyses often encode informative domain knowledge that can be useful in making the inference process more efficient. Occasionally, however, priors may be unrepresentative of the parameter values for a given dataset, which can result in inefficient parameter space exploration, or even incorrect inferences, particularly for nested sampling (NS) algorithms. Simply broadening the prior in such cases may be inappropriate or impossible in some applications. Hence our previous… 

References

SHOWING 1-10 OF 17 REFERENCES

Improving the efficiency and robustness of nested sampling using posterior repartitioning

TLDR
A posterior repartitioning (PR) method for NS algorithms is introduced, which addresses the problem of unrepresentative priors by redefining the likelihood and prior while keeping their product fixed, so that the posterior inferences and evidence estimates remain unchanged but the efficiency of the NS process is significantly increased.

Importance Nested Sampling and the MultiNest Algorithm

Bayesian inference involves two main computational challenges. First, in estimating the parameters of some model for the data, the posterior distribution may well be highly multi-modal: a regime in

Nested sampling for general Bayesian computation

Nested sampling estimates directly how the likelihood function relates to prior mass. The evidence (alternatively the marginal likelihood, marginal den- sity of the data, or the prior predictive) is

Contemplating Evidence: properties, extensions of, and alternatives to Nested Sampling

TLDR
It is established that nested sampling leads to an error that vanishes at the standard Monte Carlo rate O(N^-1/2), where N is a tuning parameter that is proportional to the computational effort, and that this error is asymptotically Gaussian.

Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses

TLDR
Three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies in very high dimensions are presented, leading to a further substantial improvement in sampling efficiency and robustness and an even more efficient technique for estimating the uncertainty on the evaluated evidence.

dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences

  • J. Speagle
  • Computer Science
    Monthly Notices of the Royal Astronomical Society
  • 2020
TLDR
Dynesty, a public, open-source, python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using the dynamic nested sampling methods developed by Higson et al, can provide substantial improvements in sampling efficiency compared to popular MCMC approaches in the astronomical literature.

Nested sampling with any prior you like

Nested sampling is an important tool for conducting Bayesian analysis in Astronomy and other fields, both for sampling complicated posterior distributions for parameter inference, and for computing

Nested Sampling Methods

TLDR
A new formulation of NS is presented, which casts the parameter space exploration as a search on a tree and ways of obtaining robust error estimates and dynamic variations of the number of live points are presented as special cases of this formulation.

Diffusive nested sampling

TLDR
A general Monte Carlo method based on Nested Sampling, for sampling complex probability distributions and estimating the normalising constant is introduced, and it is found that it can achieve four times the accuracy of classic MCMC-based Nests Sampling.

MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics

TLDR
The developments presented here lead to further improvements in sampling efficiency and robustness, as compared to the original algorit hm presented in Feroz & Hobson (2008), which itself significantly outperformed existi ng MCMC techniques in a wide range of astrophysical inference problems.