Upstream example coverage

Disposition of every notebook and script in Numerics-Python-Examples with respect to this port. “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). “Out of scope” areas were never part of the C++ port, which targets the probability, estimation, and analysis layers of Numerics plus all of RMC-BestFit.

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 fixed-parameter model and hand-picked priors not expressible; recast to mcmc_sample()
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 diagnostics on arbitrary external chains not exposed
07_integration_and_root_finding Numerical integration, root finding Out of scope the Numerics Mathematics.Integration / RootFinding namespaces are not part of the port
08_optimization Local and global optimizers Out of scope only the optimizers the estimation layer needs are ported (BFGS, Nelder-Mead, Brent, Powell, DE, MLSL), and they are internal
09_statistics Statistical tests, transforms, outliers Ported (partial) MGBT, Box-Cox/Yeo-Johnson, plotting positions, bootstrap covered; t/Mann-Whitney/KS tests and Jenks breaks are not ported
10_time_series TimeSeries container operations Out of scope the heavy Numerics TimeSeries container (interpolation, file I/O, USGS download) is a documented severance; AR/MA/ARIMA/ARIMAX models are ported
11_machine_learning K-Means, random forest, KNN, GMM Out of scope the Numerics.MachineLearning namespace is not part of the port
12_linear_models GLM regression Out of scope the Numerics.MachineLearning GLM layer is not part of the port
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/AIC instead of the unported KS test
examples/reliability_analysis.py Monte Carlo reliability Ported uses the LnNormal family in place of C# LogNormal.Base = e; results reproduce exactly