Nested Sampling (NS-AW)

Nested sampling targets the Bayesian evidence \(Z = \int \mathcal{L}(\theta)\,\pi(\theta)\,\mathrm{d}\theta\) directly and yields the posterior as a by-product. JESTER uses the BlackJAX implementation from the handley-lab fork with an adaptive Differential Evolution acceptance-walk kernel.

How it works. A set of n_live live points is maintained, all satisfying \(\mathcal{L} > \mathcal{L}^*\) for a current likelihood threshold \(\mathcal{L}^*\). Each iteration removes the n_delete_frac * n_live lowest-likelihood points (dead points), adds the same number of new points drawn by running the acceptance-walk kernel from a randomly selected live point, and advances the evidence integral. The loop terminates when the remaining evidence in the live points satisfies

\[\Delta \log Z < \texttt{termination\_dlogz}.\]

Batch deletion: Compared to the usual CPU implementation in, e.g., dynesty (as in bilby), the GPU implementation allows for batch deletion of multiple live points per iteration, which can speed up convergence at the cost of iteration granularity. An n_delete_frac of 0.5 is recommended.

Unit-cube sampling: All parameters are mapped to \([0,1]\) before sampling. Uniform parameters are rescaled linearly; MultivariateGaussianPrior parameters use the probability integral transform. Proposals wrap at the \([0,1]\) boundary via modulo.

Acceptance-walk kernel: The kernel is a bilby-style adaptive Differential Evolution walk. Starting from a live point, it proposes n_target accepted steps, taking at most max_mcmc total steps and at most max_proposals attempts per step. More details can be found in [1].

Post-processing: After the loop, dead-point weights are computed by anesthetic using the \((\log\mathcal{L}, \log\mathcal{L}_\text{birth})\) pairs. The weighted samples are then resampled to approximately ESS unweighted posterior samples for downstream use.

Configuration

sampler:
  type: blackjax-ns-aw
  n_live: 1000          # live-point population size
  n_delete_frac: 0.5    # fraction removed per iteration
  n_target: 60          # target accepted steps in acceptance walk
  max_mcmc: 5000        # max total MCMC steps per new live point
  max_proposals: 1000   # max proposal attempts per MCMC step
  termination_dlogz: 0.1

Larger n_live gives more accurate evidence estimates and denser posterior coverage at the cost of runtime. n_delete_frac trades iteration granularity against speed; the default of 0.5 matches the bilby nested-sampling setup.

API reference

• jesterTOV.inference.samplers.blackjax.nested_sampling.acceptance_walk.BlackJAXNSAWSampler

References

[1]

Metha Prathaban, David Yallup, James Alvey, Ming Yang, Will Templeton, and Will Handley. Gravitational-wave inference at GPU speed: A bilby-like nested sampling kernel within blackjax-ns. 9 2025. arXiv:2509.04336.