Population Stability Index (PSI)

Population Stability Index compares distributions by dividing a variable into bins and measuring changes in the proportion of observations in each bin. For reference share E_i and comparison share A_i, a common formula is PSI = sum_i (A_i-E_i)*ln(A_i/E_i). A contribution is zero when the shares match, and larger differences generally add more to the total. PSI is often applied to score or feature distributions in monitoring, particularly where labels arrive late. The result depends on how bins are defined. Fixed bins make comparison across time interpretable, while quantile bins based only on a reference sample can preserve baseline balance. Recomputing bins separately for each sample can make shifts harder to see. Coarse bins may hide changes within a bin; too many bins can create sparse counts and unstable ratios. If any bin has zero share, the logarithm is undefined, so implementations use smoothing or minimum proportions. Report that convention and test whether conclusions change. PSI measures distributional difference, not whether the change harms predictions. A feature can shift due to seasonality or a legitimate population change while model performance remains stable. Conversely, conditional relationships can change without a large marginal feature PSI. A score-distribution shift may indicate changed inputs, changed policy or changed model version. None of these possibilities is distinguished by the scalar index. Some domains use rule-of-thumb bands for interpreting PSI, but thresholds vary and should not be treated as universal statistical guarantees. The index is sensitive to sample size, bin count and chosen reference period. Use it as one alert signal alongside schema checks, slice metrics and delayed-label evaluation. Investigate which bins contribute to the score, whether the shift persists and whether a downstream decision changes. PSI is a compact summary for prioritizing review, not a substitute for ground-truth performance measurement or causal diagnosis.