ReconBench: joint distribution sampling

sample within the birth–death regime, then invert the log / logit transforms carefully. Check rejection rates too, otherwise the nice fitted distribution isn't necessarily what comes out the other end.

modelfit.py workflow: split parameter tables by supported birth–death regime, fit a distribution within each regime, and sample the regime according to its empirical frequency. This avoids a single one-hot mixture producing parameters inconsistent with the selected model type.

transformations: log-transform positive rate/length parameters; logit-transform proportions; retain inverse-transform metadata. Fit candidate marginals with likelihood/AIC comparison and use a Gaussian copula for dependencies. The report calls its multivariate-normal fallback unused.

Spearman and Pearson parameter-correlation matrices.

Empirical and sampled parameter distributions by birth–death model.

• sampling gates: reject unrealistic values and samples outside the recorded empirical range rule; round integer quantities; test whether a forward birth–death realization survives. The report describes validation plots from 500 samples per regime.

• review questions: exclusion/rejection changes the effective sampled distribution—save acceptance rates and before/after summaries. How are zeros/ones treated before logit transforms? Is the stated back-transform bias correction consistent with the actual marginal model? These checks are prompted by the method description, not new results.

• artifact: export the sampled parameter CSV together with regime identity, transform metadata and seed, not only plotted histograms.

Historian: best BD extinction rate versus likelihood ess.

Parameter, sampling-diagnostic, and reconstruction-score correlation matrix.