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name: posterior_two_sample_metrics description: Compute deterministic posterior two-sample diagnostics including C2ST-style accuracy for SBI benchmark recovery.

Posterior Two-Sample Metrics

Use this skill when an SBI benchmark recovery needs a lightweight distributional comparison between reference posterior samples and approximate posterior samples. It is meant for bounded runs where sklearn is unavailable but C2ST-style evidence is still needed.

Do not use this skill to reproduce the exact paper MLP C2ST when the full sklearn and benchmark runtime is available. In that case, run the official metric or an equivalent library implementation and record it as the stronger evidence.

Inputs

• JSON file with reference posterior samples.
• JSON file with approximate posterior samples.
• Optional acceptance threshold.

Outputs

• Metric JSON with c2st_accuracy, c2st_distance_to_ideal, mmd2, counts, dimension, and interpretation.

Workflow

1. Load both sample sets and validate shapes.
2. Z-score using reference-sample statistics.
3. Build a deterministic nearest-centroid classifier and evaluate it with balanced held-out folds.
4. Report balanced accuracy and its absolute distance to the ideal value 0.5. Interpret this metric by closeness to 0.5, not as either a larger-is-better or lower-is-better score.
5. Report squared distance between sample means as a small MMD-style diagnostic.

Validation

Run:

python scripts/posterior_two_sample_metrics.py self-test
python tests/test_posterior_two_sample_metrics.py

Limitations

The C2ST helper uses a deterministic nearest-centroid classifier, not the paper's MLP. It preserves the two-sample testing mechanism and interpretive scale for reduced recovery.