A distribution change that warrants review

Freeze the comparison before inspecting its result

Choose the drift preset in the report. Its twenty current observations use the same declared monthly window and complete return pairs as the reference example. Only the feature values change. The baseline contains four values of minus 1.5, six of minus 0.5, six of 0.5 and four of 1.5. The three boundaries remain minus one, zero and one throughout this comparison, rather than being refitted around the new data.

The four bins have infinite outer tails and left-inclusive, right-exclusive boundaries. A feature equal to zero belongs in the third bin; a feature equal to one belongs in the fourth. Current values are two at minus 1.2, four at minus 0.3, six at 0.6 and eight at 1.7. Keeping both the raw values and bin counts makes this convention inspectable and helps distinguish a boundary change from an observed distribution change.

Reproduce the smoothed proportions and PSI

Add alpha 0.5 to every count in both samples. Each denominator is twenty plus four times 0.5, or twenty-two. The baseline proportions are approximately 0.204545, 0.295455, 0.295455 and 0.204545. Current proportions are approximately 0.113636, 0.204545, 0.295455 and 0.386364. These are smoothed proportions, not the original sample shares. The declared smoothing avoids undefined logarithms when a bin contains no observations.

For each bin calculate its contribution as the current-minus-baseline proportion multiplied by the natural logarithm of current divided by baseline. Using full precision, the four contributions sum to 0.2024989980424936. The unchanged third-bin proportion contributes zero. The largest contribution comes from the upper tail. Retaining that decomposition is more informative than reporting a rounded score alone, because it shows which part of the fixed representation changed.

Use a second description without claiming causality

The baseline mean is zero. Its sample variance is twenty-one divided by nineteen, using the N minus one denominator, and its sample standard deviation is 1.0513149661. The current mean is 0.68. Dividing the mean difference by the baseline sample standard deviation gives 0.6468090172. NIST's statistical handbook supports the sample-deviation convention; it does not prescribe a decision threshold for this particular synthetic feature or certify that its distribution is appropriate.

The score exceeds the example review threshold of 0.10 and remains below escalation at 0.25, so the report requests review. These are selected teaching-policy levels. They are neither a statistical significance test nor universal limits. The inputs do not identify whether a real change would come from sampling variation, a data pipeline correction, population composition, changed market conditions or a changed relationship between features and future outcomes.

Investigate without erasing the reference

A useful review would first check feature definition, units, period population and source transformations, then inspect the upper-tail observations. The synthetic return series is unchanged and remains fully measurable. That does not establish that drift is harmless: it only shows that this constructed case does not alter those supplied outcomes. The feature comparison and outcome comparison answer different questions, and neither can stand in for an independently designed validation study.

Export the full input and report before experimenting with a different baseline or policy. Comparing the current sample with itself would mechanically reduce PSI to zero without explaining the original change. The fictional change register therefore defers a baseline replacement until an independent rationale and prospective effective date exist. Preserve the original reference, bins, smoothing and report so a reviewer can replay the same comparison after any proposed update.

Keep in the decision record

• Freeze bins and disclose smoothing before comparing distributions.
• PSI and mean shift describe changes without explaining their causes.
• Changing the baseline requires evidence beyond obtaining a smaller score.

Source notes

1. NIST statistical handbook: measures of scale
2. Federal Reserve: model risk guidance, applied within its scope

Sources inform the stated methods and governance context. All example monitoring observations are synthetic. No regulatory approval or production monitoring certification is implied.

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