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---
name: posterior_mmd_recovery
description: Compute squared MMD for posterior samples and package score-based SBI recovery-result metadata.
---
# Posterior MMD Recovery
Use this skill when evaluating posterior samples from a score-based SBI recovery against true, analytic, or reference posterior samples. It owns the metric calculation and target-metadata preservation.
## Inputs
- Recovered posterior samples.
- Reference posterior samples.
- Target metadata from `module_plan.json.fast_recovery_target`.
- Mechanism checks generated by recovery.
## Outputs
- Squared MMD using a Gaussian kernel with median-distance bandwidth.
- A threshold decision for reduced recovery.
- Recovery-result JSON fields that keep the module-plan target unchanged.
## Workflow
1. Validate that recovered and reference sample arrays are non-empty and have matching dimension.
2. Compute pairwise squared distances and median-heuristic bandwidth.
3. Compute stable biased squared MMD.
4. Copy target metadata exactly into the recovery result.
5. Record mechanism checks separately from the numeric metric.
## Validation
Run `python tests/test_posterior_mmd_recovery.py` or the Distiller skill-tree validator.
## Limitations
A low MMD is not sufficient evidence for proxy acceptance unless mechanism checks also prove the paper's score-training, score-composition, and sampling contracts were exercised.
