Upstream example coverage

Disposition of every notebook and script in Numerics-Python-Examples with respect to this port. Every upstream topic is now covered. “Ported” examples reproduce the upstream results (exactly where seeded and deterministic). “Recast” examples cover the same statistical content through this package’s public API, where the upstream code drove the C# classes directly in ways this API deliberately does not expose (notably custom prior lists and Python-callback likelihoods), or where the material moved onto a page of this site that organizes it differently.

Upstream	Topic	Status	Notes
00_getting_started	Loading the library, first distribution	Ported	pythonnet/DLL plumbing replaced by a plain package install
01_distributions	Distribution tour, sampling, Latin hypercube	Ported	all 10 families and the seeded draws reproduce exactly
02_distribution_fitting	MOM / MLE / L-moment fitting	Ported	fitted parameters reproduce exactly
03_mcmc_basics	RWMH fundamentals	Recast	recast onto mcmc_sample(), which fits a named family under constraint-based priors; the hand-written likelihood and hand-picked priors this notebook uses are reachable through mcmc_posterior() (example 14)
04_mcmc_bayesian_inference	Bayesian flood frequency	Ported	same priors, seed, and serial chains as upstream; acceptance streams bit-exact vs C#, posterior tables reproduce at displayed precision (documented ulp drift in the MAP optimizer)
05_mcmc_adaptive	Adaptive sampler comparison	Recast	PyMC benchmark sections dropped
06_mcmc_diagnostics	R-hat, ESS, autocorrelation	Recast	R-hat and ESS come back with the fit rather than as verbs of their own, so there is no way to score a chain the package did not produce; autocorrelation() does take any series
07_integration_and_root_finding	Numerical integration, root finding	Recast	both namespaces ported in v0.9.0; quadrature() covers ten deterministic rules plus three seeded Monte Carlo families, root_find() four methods; example 18 runs them over its own functions rather than this notebook’s
08_optimization	Local and global optimizers	Recast	all fourteen optimizers are public through optim_minimize()/optim_maximize() as of v0.10.0, constrained optimization included; example 13 fits a rating-curve likelihood and example 19 covers the global, constrained, and network methods, neither reproducing this notebook’s specific test functions
09_statistics	Statistical tests, transforms, outliers	Ported	MGBT, Box-Cox/Yeo-Johnson, plotting positions, and bootstrap here; the thirteen hypothesis_test() statics and the paired-data curves in example 28; Jenks breaks as ml_jenks_breaks() in example 29
10_time_series	TimeSeries container operations	Ported	the container landed in v0.13.0; file I/O and the USGS download stay out, everything else is public through time_series() and the ts_*() verbs
11_machine_learning	K-Means, random forest, KNN, GMM	Ported	the whole Numerics.MachineLearning namespace landed in v0.12.0 as the eight ml_*() verbs
12_linear_models	GLM regression	Ported	ml_glm(), all five families selected by link
examples/bayesian_regression.py	DEMCzs linear regression	Recast	recast onto arimax_analysis with a linear trend
examples/flood_frequency_analysis.py	Distribution ranking, design flows	Ported	fits and return-period tables reproduce exactly; ranking by log-likelihood and AIC rather than the KS test, which does not penalize GEV’s extra parameter
examples/reliability_analysis.py	Monte Carlo reliability	Ported	uses the LnNormal family in place of C# LogNormal.Base = e; results reproduce exactly

Beyond the upstream examples

These examples cover ground the upstream notebooks never reach, most of it RMC-BestFit and the rest the callback surface, so they have no upstream counterpart and no upstream outputs to reproduce against. Each still ends in an executable check, and each pair asserts the same literals in R and Python, which is what pins the cross-language identity.

Example	Covers
12. Model evaluation	goodness_of_fit(), gof_test() (KS/AD), gof_rmse(), aic()/aic_weights(), and classification_metrics(), ranking four candidate distributions against the same record example 21 uses
13. A custom objective	optim_minimize()/optim_maximize() over a hand-written likelihood the port does not otherwise know how to fit; global ("de") versus local ("bfgs") optimization, and the sign convention of optim_maximize()’s reported value
14. A custom posterior	mcmc_posterior() over a log-likelihood and priors you write, reaching all eight samplers – Gibbs included, which needs a proposal function and so had been unreachable from either package
15. A custom bootstrap	bootstrap_custom() over the four upstream delegates and all five interval methods, putting an interval on a statistic no verb computes; drawing inside resample from the handle the replicate passes in
16. Ranking fifteen candidate families	fit_distributions() on its own terms: what the fifteen candidates are, why AIC, BIC and RMSE can each name a different winner, and reading the converged column
17. A pivotal bootstrap	bootstrap_custom(run_type = "pivotal"), the covariance-aware run type: the fit_with_covariance function it adds, both interval blocks it reports, the six replicate counts in pivotal_diagnostics, and standardizing in link space
23. Censored flood frequency	historical and paleoflood interval observations, perception thresholds, Hirsch-Stedinger plotting positions, Multiple Grubbs-Beck low outliers
24. Nonstationary frequency analysis	trends on a distribution parameter, stationary versus nonstationary model comparison by AIC, BIC, and DIC
25. Estimation methods	fit_mle, fit_map, fit_bayesian, and fit_gmm on the same censored record; AIC/BIC/DIC, profile versus credible intervals, R-hat/ESS, and estimation diagnostics
26. Copulas and joint frequency	bivariate copulas fitted by pseudo-likelihood, Kendall’s tau, and inference from margins; tail dependence; and-joint exceedance of a coincident event; the multivariate normal rectangle probability; cross-check against bivariate_analysis
27. Composite distributions	two-component mixtures through model_mixture and fit_mle rebuilt as dist_mixture; kernel density with an explicit bandwidth and bounded_by_data; dist_truncated renormalization onto a physical range
28. Hypothesis tests and paired data	hypothesis_test() and the analysis_data_hypothesis_test()/analysis_data_statistics() DataFrame facades on a flood record; correlation()’s matrix form; the Paired Data curve subsystem – curve_interpolate(), curve_area(), curve_simplify()’s three algorithms, and uncertain_curve_sample()