Interpreting results

A run produces three things. A per-member weights table, an SLE projection, and a set of convergence diagnostics. The weights and the projection are only meaningful if the sampler that produced them converged. So start with the diagnostics.

Did the run converge?

The member weights come from a posterior estimated by MCMC (NUTS). If the chains did not converge, the weights are unreliable. So is every number downstream of them, however plausible they look.

fusion.run checks this for you. It emits a fusion.ConvergenceWarning when something is off:

ConvergenceWarning: max R-hat 1.043 exceeds 1.01. Chains have not converged;
increase inference.tune/draws.

You can also inspect the numbers directly. Every Result carries them. sampler_diagnostics works on any trace:

import fusion

result = fusion.run(cfg)
result.diagnostics
# {'max_rhat': 1.002, 'min_ess_bulk': 1840.0, 'min_ess_tail': 1610.0, 'n_divergences': 0.0}

fusion.sampler_diagnostics(result.trace)   # same dict, callable on any InferenceData

What the numbers mean

Key	What it measures	Healthy
max_rhat	Worst-case Gelman–Rubin R-hat across the four sampled parameters (sigma_base_thick, sigma_base_vel, beta_thick, beta_vel). It compares between-chain and within-chain variance. A value above 1.01 means the chains disagree.	≤ 1.01
min_ess_bulk	Smallest bulk effective sample size. This is how many effectively-independent draws inform the center of the posterior.	hundreds or more
min_ess_tail	Smallest tail effective sample size. Same idea, for the distribution's tails. The projection's credible interval rests on these.	hundreds or more
n_divergences	Count of divergent transitions. A divergence means the sampler hit a region it could not integrate accurately. The posterior may be biased, not just noisy.	0

These four diagnostics are also written into run_metadata.json. A saved run therefore records whether it converged.

What to do when a check fails

Symptom	Fix
max_rhat above 1.01, or low min_ess_*	Raise inference.tune and/or inference.draws, then rerun.
n_divergences above 0	Raise inference.target_accept (e.g. 0.95 to 0.99). If divergences remain, also raise tune.
Big gap between posterior_mean and point_estimate in the weights table	This is a symptom of poor convergence. Check the diagnostics above before trusting the weights.

This is not the same as weight stability

fusion.sampler_diagnostics asks one question. Did the MCMC chains converge? A separate helper, fusion.weight_stability_across_seeds, asks a different one. How sensitive are the weights to which 20k pixels were subsampled? It answers by comparing several runs with different inference.subsample.seed values. A run can converge cleanly and still have subsample-sensitive weights, or the reverse. Check both before reporting.

The weights table

fusion.save_weights(result, "weights.csv") writes one row per ensemble member:

Column	Meaning
member_id	Member label (e.g. run07), parsed from the ensemble filename.
posterior_mean	Mean of the member's Bayesian weight w over the posterior. This is the headline skill weight. It sums to 1 across members.
posterior_sd	Spread of w across posterior samples. This is the uncertainty on that weight.
point_estimate	The prototype's plug-in weight: softmax of the per-member log-likelihood at the posterior-mean parameters. It is deterministic, and close to posterior_mean when the chains converged.
point_estimate_loglik	The N-scaled per-member Gaussian log-likelihood, before the softmax. This is the raw goodness-of-fit. Use it to compare relative fit between members. It is not a weight.

Which to use: report posterior_mean with posterior_sd as its uncertainty. Use point_estimate as a cross-check, per the table above.

The projection

result.projection is the weighted sea-level-equivalent (SLE) distribution at projection.target_year. It holds one value per posterior sample. Each member's projected SLE is weighted by its skill weight. Report it as a central estimate plus a credible interval, not a bare mean:

fusion.projection_summary(result.projection)
# {'median': 0.071, 'mean': 0.072, 'sd': 0.011, 'lower': 0.054,
#  'upper': 0.091, 'lower_q': 0.05, 'upper_q': 0.95}

fusion.plot_projection(result, "sle_2100.png")   # histogram with median + 5–95% CI

Quote the median with the 5–95% credible interval (lower to upper).

Projection magnitudes are provisional

The member to SLE reduction in v1 is a placeholder. It is a mean of ice thickness, not the real volume-above-flotation calculation. Until that lands, treat the projection's shape and relative spread as illustrative. Do not read the absolute SLE magnitude as physically meaningful. The weighting itself, the weights table, is validated and unaffected.