Proposal: Integrating advanced statistical inversion and uncertainty quantification modules

[Zoltan1970]

Hi welltestpy maintainers,

I'm a hydrogeologist from Brazil currently developing a Python suite for aquifer parameter estimation from pumping tests, and I'd like to explore whether there's interest in collaboration or integration with welltestpy.

I have completed two modules so far — one for the Neuman (1974) unconfined aquifer solution and one for Dupuit-Thiem steady-state cone of depression — and I'm working toward a full suite covering Theis, Hantush, Cooper-Jacob, and others.

Beyond the analytical solutions themselves, the focus of my work is on statistical rigor in the inversion, which I believe is complementary to welltestpy's geostatistical approach:

• Log-weighted objective function with analytical justification and Wilcoxon superiority test
• Block bootstrap for autocorrelated residuals (AR(1)), with IQR-based outlier removal
• Correct AIC/BIC/AICc via Gaussian log-likelihood (separate from the optimization objective)
• Structural correlation matrix from prior-free bootstrap, exposing real equifinality
• MAP Bayesian estimation with isolated prior weight (reproducible across runs)
• Residual normality tests (Shapiro-Wilk / Anderson-Darling) with automatic flags
• Fisher Information ellipsoid with eigendecomposition for identifiability diagnostics
• Full Monte Carlo uncertainty propagation with auditable per-parameter distributions

I see a potential fit as a statistical estimation layer that could complement welltestpy's existing parameter estimation infrastructure, similar to how anaflow provides the type curves.

Before investing time in code adaptation, I wanted to open a conversation: Is there interest in this direction? Would a separate package that integrates with welltestpy be the right approach, or would you prefer a direct contribution to the estimate subpackage?

Happy to share the code for review.

Best regards

Zoltan Romero C. Rodrigues.