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name: particle_mirror_descent_mixture_protocol description: Use this skill to construct the synthetic tied Gaussian mixture posterior target from the Particle Mirror Descent paper, including data generation, log prior/likelihood functions, and grid posterior evaluation.

Synthetic Mixture Model Protocol

When To Use

Use this skill when a recovery or experiment needs the paper's synthetic multimodal Bayesian target. Do not use it to run PMD updates or score a completed density estimate.

Inputs

• Random seed and observation count.
• Optional model constants: theta_true=(1,-2), sigma1=1, sigma2=1, sigma_x=2.5, mix_prob=0.5.
• Optional grid bounds for posterior evaluation.

Outputs

• Generated observations and provenance metadata.
• Stable log_prior, log_likelihood, and dataset log posterior functions.
• Normalized target posterior density on a two-dimensional grid.
• Expected symmetric mode locations.

Workflow

1. Generate observations from the tied two-component Gaussian mixture described in Section 6.
2. Evaluate likelihoods with log-sum-exp to avoid underflow.
3. Combine independent Gaussian priors and the full-data likelihood into an unnormalized posterior.
4. Normalize grid posterior arrays before downstream metric computation.
5. Save generated data provenance when used in recovery.

Validation

Run:

python tests/test_mixture_protocol.py

Limitations

This skill provides a reduced synthetic protocol, not the paper's full repeated 1000-sample comparison against all baselines.