Posterior Mmd Recovery

---
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.