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Summary
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This study enhances Bayesian log-evidence calculation by transforming prior volume estimation into a Bayesian inference problem, improving accuracy for nested sampling (NS) with fewer than 100 samples.

Keywords:
Bayesian inferenceevidence calculationinformation field theorynested sampling

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Area of Science:

  • Computational Statistics
  • Bayesian Inference
  • Machine Learning

Background:

  • Nested sampling (NS) is a stochastic method for computing log-evidence in Bayesian analysis.
  • Current NS methods are limited by the accuracy of stochastic prior volume estimations.
  • Inaccurate volume estimates directly impact the precision of the log-evidence calculation.

Purpose of the Study:

  • To improve the accuracy of log-evidence calculation in Bayesian problems using nested sampling.
  • To address limitations in current nested sampling by enhancing prior volume estimation.
  • To develop a post-processing method for nested sampling that refines volume estimates.

Main Methods:

  • Transformed prior volume estimation into a Bayesian inference problem.
  • Incorporated a smoothness assumption for likelihood-prior-volume relationships.
  • Developed a post-processing algorithm providing posterior samples of the likelihood-prior-volume relation.

Main Results:

  • Demonstrated significant accuracy improvements in log-evidence calculation compared to plain NS.
  • Observed enhanced performance particularly for NS runs with fewer than 100 active samples.
  • Identified potential numerical challenges with the method when exceeding this sample threshold.

Conclusions:

  • The proposed Bayesian inference approach for volume estimation enhances nested sampling accuracy.
  • This method offers a valuable post-processing step for refining log-evidence calculations.
  • The technique shows promise for Bayesian computation, especially in resource-constrained scenarios.