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name: posterior_sample_approximation description: Fit compact posterior approximations from SBI simulator pairs and emit posterior samples with optimizer traces.

Posterior Sample Approximation

Use this skill when an SBI recovery needs approximate posterior samples from simulation pairs and a fixed observation. It is designed for bounded reduced experiments where a full neural density estimator is unavailable, but the run must still perform an actual optimizer step and return posterior samples.

Do not use this skill as a substitute for a full neural SBI algorithm when that runtime is available. It is a reduced mechanism-preserving approximation.

Inputs

• Simulation JSON with theta and x arrays.
• Conditioning observation vector.
• Training settings: learning rate, number of steps, seed.
• Posterior sampling settings: sample count and sample variance.

Outputs

• Approximate posterior sample JSON.
• Training trace with before/after loss and before/after trainable parameters.

Workflow

1. Load simulator pairs created by the task protocol skill.
2. Fit an affine map from observations to parameter means with gradient descent.
3. Record loss_before, loss_after, params_before, params_after, and optimizer_state_changed.
4. Condition the fitted map on the target observation.
5. Draw approximate posterior samples around the predicted mean.
6. Save the sample file and training trace for the recovery validator.

Validation

Run:

python scripts/posterior_sample_approximation.py self-test
python tests/test_posterior_sample_approximation.py

Limitations

This script implements a small affine posterior mean model with diagonal Gaussian sampling noise. It demonstrates the benchmark mechanism and optimizer evidence, but it is not a normalizing-flow posterior estimator.

The optimizer_state_changed flag is evidence-bearing: a zero-step or otherwise frozen run must leave it false, with identical params_before and params_after.