Characterization of the null distribution for information-theoretic significance testing

Determine the underlying null distribution of the proposed sample path causal measure for assessing information flow from respiration or other auxiliary signals to RR intervals.

Background

The proposed framework uses the sample path causal measure to quantify directed information between auxiliary physiological signals and RR intervals. Statistical significance is assessed through permutation testing because the distribution of the measure under the null hypothesis is not established.

Determining the null distribution would clarify the theoretical basis of significance testing and could provide an alternative to the computationally expensive generation of permutation samples.

References

In order to assess significance, because the underlying null distribution is unknown, we utilize permutation testing to generate samples to do so.

— Efficient Convex Optimization Methods for State-Space Heartbeat Dynamics Models with Gamma Generalized Linear Models  (2610.00884 - Liu et al., 1 Oct 2026) in Section 6, Discussion, paragraph beginning “Beyond model fitting”