Effect of oscillatory dynamics on sampling efficiency

Determine the effect of imposing oscillatory dynamics through the choice of the periodic function \(g\) on the sampling efficiency of the temporal point-process sampler, including metrics such as mixing time and asymptotic variance.

Background

The sampler permits the choice of a periodic base-process function $g$, which can induce oscillatory dynamics while preserving the target distribution as the limiting distribution. The paper does not analyze how these oscillations affect the efficiency of sampling.

The authors distinguish between common modulation of all components, which can be interpreted as a nonlinear rescaling of time, and relative modulation across components, which may alter the effective scan order and therefore the sampler’s mixing behavior. They explicitly identify the impact on efficiency as unresolved and conjecture that the choice of $g$ can affect efficiency metrics.