Calculate PSI with frozen bins and visible counts

Define the partition before the comparison

The report accepts explicit increasing bin edges and applies the same edges to baseline and current features. With edges minus one, zero and one, the four bins are below minus one, from minus one to below zero, from zero to below one, and one or above. The tails extend without artificial finite limits.

Bins are left-inclusive and right-exclusive. A feature exactly equal to zero enters the bin beginning at zero. This boundary rule matters when values are discrete or rounded. A reviewer should be able to assign every fixture value to a bin manually and reproduce the counts without relying on a charting library’s automatic histogram choices.

Retain the exact edge array with every exported report so later comparisons cannot silently adopt a different partition.

Reproduce the report’s synthetic comparison

The reference baseline has counts 4, 6, 6 and 4 across the four bins, for twenty observations. The drift scenario has counts 2, 4, 6 and 8. With smoothing alpha equal to 0.5, each denominator is twenty plus four times 0.5, or twenty-two.

The smoothed baseline proportions are 4.5/22, 6.5/22, 6.5/22 and 4.5/22. Current proportions are 2.5/22, 4.5/22, 6.5/22 and 8.5/22. Summing each difference multiplied by the natural logarithm of its proportion ratio gives PSI approximately 0.202499. These invented counts reproduce an illustrative distribution comparison, not an observed investment signal.

Read the individual contributions

The formula is sum of (q minus p) times log(q divided by p), using current proportions q and baseline proportions p. With positive proportions, each contribution is nonnegative. Identical bin proportions give zero. A large contribution identifies a bin worth inspecting, but it does not identify a causal mechanism.

In this example the highest bin gains four observations, while the lowest two lose observations. Inspect those original values and their period keys. A unit conversion, source change or genuine change in the measured environment can produce similar count movements. PSI cannot distinguish those explanations merely because one bin dominates the score.

Keep thresholds in their proper role

Yurdakul and Naranjo analyze PSI’s statistical properties and warn that familiar rule-of-thumb boundaries do not themselves specify error rates. The publication uses 0.1 and 0.25 only as editable example policy values. They are not regulatory limits, universal stability definitions or empirically calibrated thresholds for an investment model.

At the reference policy, 0.202499 triggers review but not the higher PSI escalation threshold. Changing a threshold changes that workflow label without changing the distribution. Keep the numeric result and policy version together so readers can distinguish a changed observation from a changed response rule.

Understand the information the partition discards

PSI sees bin membership rather than every numerical movement. A feature moving from 1.1 to 100 remains in the upper tail bin. Conversely, a small movement across zero can change counts. NIST’s histogram guidance explains the basic distribution summary; the choice to freeze these particular bins is part of this report’s documented design.

The engine withholds drift for duplicate or unexpected periods, fewer than ten numeric current features, or zero baseline sample deviation. Missing expected rows can leave a labeled observed-subset result. Even a fully calculated score is descriptive: it does not establish concept drift, a performance forecast or permission to approve a model.

Keep in the decision record

• Freeze boundaries and boundary inclusivity before comparing samples.
• Retain counts, smoothing and policy beside PSI.
• A workflow threshold is not a universal statistical test.

Source notes

1. Yurdakul and Naranjo — Statistical properties of the population stability index, Journal of Risk Model Validation 14(4)
2. NIST/SEMATECH e-Handbook — Histogram
3. Rabanser, Günnemann and Lipton — Failing Loudly, NeurIPS 2019

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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