Universal effective-sample-size superiority over birth-death samplers

Determine whether the temporal point-process sampler always has a greater multivariate effective sample size than the corresponding birth-death sampler, regardless of the target distribution.

Background

The simulation study compares the temporal point-process sampler with a birth-death sampler obtained by adding uninformative service-time randomness. Across all 63 tested target distributions, the point-process sampler has a higher effective sample size, which the authors interpret as evidence of a momentum-like effect caused by deterministic service times and the resulting inability to immediately backtrack.

The conjecture asks whether this empirical advantage in multivariate effective sample size is universal across target distributions, rather than limited to the finite collection and parameter regimes examined in the simulations.

References

For these reasons, we conjecture that the point process sampler may always have a greater ess than the birth-death sampler, regardless of the target distribution.

— Sampling on Discrete Spaces with Temporal Point Processes  (2603.09089 - Stewart et al., 10 Mar 2026) in Section 5, subsection “Commonly observed behaviour”