Statisticsml-monitoringPython

Bayesian drift detection for feature pipelines

A compact note on using posterior predictive checks to catch quiet distribution shifts before model quality moves.

2026-02-187 min readpublishedMedium

Feature drift is rarely a single dramatic event. In production it usually arrives as a small shift in event mix, a change in freshness, or a schema field that is technically valid and semantically wrong.

For a binary feature, a beta-binomial model gives a lightweight first pass:

p(\theta \mid x, n) \propto \theta^{x+\alpha-1}(1-\theta)^{n-x+\beta-1}

Operational rule

Alert when the posterior predictive probability of the latest window falls below a threshold and the data freshness service agrees the window is complete.

The useful piece is not the equation itself. It is the contract around it: define the reference population, freeze the time window, and make the model explain which feature moved.

from scipy.stats import betabinom
 
def posterior_tail_probability(successes, trials, alpha=2, beta=8):
    observed_rate = successes / trials
    expected = betabinom.cdf(successes, trials, alpha, beta)
    return min(expected, 1 - expected), observed_rate

Median detection lag

2.4 windows

In synthetic backtests with 5% absolute rate shifts

Posterior mass

prior -> posterior

The final dashboard should show the posterior, the raw feature count, and the lineage of the upstream job. Statistical confidence without data lineage tends to create very polished confusion.