test jev calibration with ece and brier score

Start with One Fixed Probabilistic Event

For a Noul, the event is its yes condition. For a Choice, evaluate each option one-vs-rest or use a multiclass proper scoring rule; do not treat the winning probability alone as the entire distribution. For Score, decide whether the target is each ordinal level, a cumulative event such as “at least high,” or the weighted summary. Publish that choice.

The examples must be representative of deployment and labeled without using Jev’s output as truth. Freeze model, provider, question, criteria and state projection. Use grouped or time-based splitting when duplicate users, documents or evolving traffic could leak information.

Reliability Diagram Procedure

Equal-width bins make probability regions easy to compare but may leave sparse extremes. Equal-count bins stabilize counts but use different probability widths. Report which method was used and show counts; otherwise two ECE values or plots may look comparable when they are not.

1. Collect pairs (p_i, y_i) where p_i is the predicted event probability and y_i is 0 or 1.
2. Choose fixed-width or equal-count bins before inspecting the desired conclusion.
3. For each bin, calculate mean prediction, empirical positive rate and sample count.
4. Plot empirical rate against mean prediction with the diagonal as perfect calibration.
5. Add uncertainty intervals and repeat for important populations and time windows.

Brier Score Preserves Every Probability Error

For probabilities [0.9, 0.7, 0.4, 0.2] and outcomes [1, 0, 1, 0], squared errors are [0.01, 0.49, 0.36, 0.04]; the Brier score is 0.225. Lower is better. Always compare with a meaningful baseline such as the training-set base rate and provide a confidence interval.

Brier score captures both calibration and discrimination, so it cannot by itself say why one model wins. Decompose the result or read it alongside a reliability plot and task metrics. A system can improve ranking while worsening calibration, or vice versa.

brier = (1 / n) * sum((p_i - y_i) ** 2 for i in range(n))

ECE Is a Summary with Analyst-Controlled Choices

Expected calibration error averages the absolute calibration gap across bins, weighted by bin population. It is readable but sensitive to bin count, boundaries and sample size. A low aggregate ECE can hide severe error in a rare high-risk slice or cancellation that becomes visible only in the plot.

Publish the exact binning implementation, minimum count and handling of empty bins. Do not rank models from tiny ECE differences without uncertainty analysis. If action thresholds sit near 0.8, inspect local calibration and error around that region rather than trusting a global average.

ECE = sum((n_b / n) * abs(observed_rate_b - mean_probability_b) for each bin b)

Add Intervals and Paired Comparisons

Bootstrap examples to estimate intervals for Brier score, ECE and threshold metrics, preserving groups when several rows come from one user or document. When comparing two evaluators, resample paired examples so the interval reflects their difference on the same cases. Sparse slices may need more data rather than a more confident chart.

Pre-register primary metrics and report all planned slices. Repeatedly changing bins, thresholds or excluded examples after seeing results creates researcher degrees of freedom and optimistic claims. The general Jev calibration guide covers dataset and monitoring design.

Translate Calibration into Selective Risk

For each candidate action threshold, calculate coverage and error among automatically acted cases, plus missed positives, review volume and expected cost. Plot risk against coverage. This answers the deployment question ECE cannot: how much traffic can the system handle at an acceptable observed error rate?

Keep final threshold selection on a calibration split, then report once on the holdout. Follow Jev thresholds for error-cost decisions and abstention and human review for queue design.