Nonlinear Search
Model-family comparison covers kernel smoothing, polynomial regression, sinusoidal regression, and Fourier-series regression with explicit complexity tuning.
Methods Evidence
Statistical Methods Evidence
Public-safe evidence documenting statistical methods that I apply in analysis work: nonlinear model search, Fourier regression, interpretable GLMs, validation, calibration, and threshold analysis. The artifacts are derived from graduate statistics coursework.
Statistics Evidence
Coursework methods applied to analytics work
The repo turns private coursework artifacts into public-safe, runnable methods evidence with clean titles, sanitized data, generated figures, model-comparison tables, and skill summaries.
Evidence Packet
- Nonlinear signal modeling and extrapolation
- Kernel smoothing benchmark and polynomial model path
- Sinusoidal and Fourier-series regression with grid search
- Clinical risk GLM sequence with repeated stratified 5-fold CV
- Log-loss selection with Brier score, AUC, AIC, and BIC checks
- Calibration and threshold operating-characteristic analysis
- Sanitized public datasets and reproducible R scripts
- Public-safety validation target in the Makefile
Methods
What reviewers can inspect
Extrapolation Judgment
The nonlinear project separates high in-sample fit from plausible behavior beyond the observed range and reports residual diagnostics for the selected model.
GLM Validation
The clinical project compares staged logistic models with repeated stratified cross-validation and selects the primary model by probability-scale log loss.
Decision Metrics
The risk model includes calibration tables and threshold metrics, including sensitivity, specificity, PPV, and NPV at candidate review cutoffs.
Methods Index
Method-to-artifact map
Each row links a demonstrated statistical method to the public-safe artifact where the method can be inspected.
| Method | Source project | Proof artifact |
|---|---|---|
| Model family search | Exam 1: nonlinear signal modeling | nonlinear_model_search.csv |
| Grid search / parameter sweep | Exam 1: nonlinear signal modeling | nonlinear_fourier_grid.csv |
| Complexity tuning | Exam 1: nonlinear signal modeling | nonlinear_polynomial_path.png |
| Basis expansion | Exam 1: nonlinear signal modeling | nonlinear_signal_modeling.R |
| Polynomial regression path | Exam 1: nonlinear signal modeling | nonlinear_model_search.csv |
| Incremental R-squared / elbow analysis | Exam 1: nonlinear signal modeling | nonlinear_polynomial_path.png |
| Adjusted R-squared | Exam 1: nonlinear signal modeling | nonlinear_model_search.csv |
| AIC/BIC model comparison | Exam 1: nonlinear signal modeling | nonlinear_model_search.csv |
| Harmonic / Fourier-series regression | Exam 1: nonlinear signal modeling | nonlinear_fourier_fit.png |
| Frequency tuning | Exam 1: nonlinear signal modeling | nonlinear_fourier_grid.csv |
| Residual diagnostics | Exam 1: nonlinear signal modeling | nonlinear_diagnostics.png |
| Extrapolation plausibility check | Exam 1: nonlinear signal modeling | nonlinear_summary.md |
| Nonparametric smoothing benchmark | Exam 1: nonlinear signal modeling | nonlinear_kernel_estimates.csv |
| Candidate model comparison | Final: clinical risk GLM | clinical_model_comparison.csv |
| Nested / staged model building | Final: clinical risk GLM | clinical_summary.md |
| Repeated stratified k-fold cross-validation | Final: clinical risk GLM | clinical_risk_glm.R |
| Primary metric selection: CV log loss | Final: clinical risk GLM | clinical_model_comparison.csv |
| Secondary metrics: Brier, AUC, AIC, BIC | Final: clinical risk GLM | clinical_model_comparison.csv |
| Spline terms | Final: clinical risk GLM | clinical_risk_glm.R |
| Interaction tests | Final: clinical risk GLM | clinical_model_comparison.csv |
| Flexible benchmark model: classification tree | Final: clinical risk GLM | clinical_tree_tuning.csv |
| Hyperparameter tuning grid | Final: clinical risk GLM | clinical_tree_tuning.csv |
| Calibration analysis | Final: clinical risk GLM | clinical_calibration.png |
| Threshold analysis | Final: clinical risk GLM | clinical_thresholds.csv |
| Sensitivity model retained for interpretation | Final: clinical risk GLM | clinical_summary.md |
Inspect In Source Repo
Runnable public methods packet
The repo uses a `make all` pipeline to regenerate public data where appropriate, run analyses, build figures and report summaries, and validate the public boundary.
Safety Boundary
Curated methods derivative
The project publishes public-safe analysis code, sanitized data, generated figures, and method summaries. It does not publish private course prompts, syllabi, lecture material, source documents, or direct clinical record identifiers.