Slow IID test progress

Indications for (un)successful slow IID test.

Indications for (un)successful slow IID test.

A. Current rank of normalised test statistic (versus ratio = 1.0). This should be quickly tending towards 100.

B. Current permutation number. Total number of permutations = permutation number x no. of utilised CPU cores.

C. Number of seconds remaining for the test to fully complete with all 10,000 permutations. If the rank is not quickly tending towards 100, it is just as well to abort the test and amend the $(\epsilon, \tau)$ sampling methodology. Increase the sampling resolution ($\downarrow \epsilon$) or decrease the sample rate ($\uparrow \tau$). Otherwise, an entropy estimate by strong compression will be required as the samples will be non-IID. This will result in lower bounds of certainty of $H$.

D. The normalised test statistic (NTS). Ideally for good IID samples, NTS will oscillate between >1 and <1, or the leading digit will oscillate between 1 and 0. Such oscillation will allow the current rank to quickly tend to 100. NTS will mainly remain >1 for data samples that do not exhibit IID characteristics as they will not compress well when randomly permuted. Rather than waiting for full test completion (C) in that case, the test can be aborted and the sampling methodology amended.