---

name: particle_mirror_descent_density_metrics description: Use this skill to score Particle Mirror Descent density approximations against reduced posterior targets with total variation, cross entropy, and symmetric mode coverage diagnostics.

Posterior Density and Mode Metrics

When To Use

Use this skill after a PMD or proxy density run has produced particles, weights, grid densities, or explicit mode locations. Do not use it to generate observations or update particles.

Inputs

• Particle locations and normalized weights.
• Expected posterior mode coordinates and a radius for reduced mode checks.
• Optional grid target and estimated density arrays with a cell area.

Outputs

• total_variation and cross_entropy for grid densities when available.
• Per-mode mass, mass ratio, effective sample size, and mode_coverage_score.
• Mechanism-check booleans suitable for recovery validation.

Workflow

1. Confirm weights are nonnegative and normalized within numerical tolerance.
2. Accumulate particle mass inside each expected mode ball.
3. Convert balanced multimodal support into mode_coverage_score.
4. For grid inputs, compute total variation and cross entropy with a shared cell area.
5. Emit mechanism checks that distinguish metric success from actual PMD execution.

Validation

Run:

python tests/test_density_metrics.py

Limitations

The mode score is a reduced synthetic proxy for the paper's full figure-level total variation and cross-entropy comparisons. It should be interpreted only with the recorded PMD trace.