ODR Bootstrap

Orthogonal Distance Regression with Bootstrap Resampling for SIMS Calibration

A Python package for robust calibration curve fitting with proper uncertainty quantification in both x and y measurements.

Overview

What is ODR Bootstrap?

When fitting calibration curves to scientific data, measurement errors exist in both the independent variable (x, e.g., concentration) and dependent variable (y, e.g., ion intensity). Ordinary least squares regression assumes errors only in y, leading to biased fits.

Orthogonal Distance Regression (ODR) properly accounts for uncertainties in both x and y. Bootstrap resampling estimates confidence intervals by repeatedly refitting the model to random subsamples of the calibration data.

This package combines these techniques for publication-ready uncertainty quantification in SIMS (Secondary Ion Mass Spectrometry) calibration analysis.

Features

✅ NumPy-style documentation for all functions
✅ 22 comprehensive unit tests (100% pass rate)
✅ Runnable example workflow with synthetic data
✅ Compatible with scipy 1.15+ (deprecated API updates)
✅ Zero-intercept fits with proper parameter handling
✅ Publication-ready calibration plots

Installation

With UV (recommended)

uv pip install odr-bootstrap

With pip

pip install odr-bootstrap

From source

git clone https://github.com/whtowbin/odr-bootstrap.git
cd odr-bootstrap
uv sync
# or
pip install -e .

Documentation

Full documentation is available at Read the Docs.

For quick reference, see:

• API Reference
• Tutorial & Examples
• Examples Directory

Quick Start

import numpy as np import matplotlib.pyplot as plt from odr_bootstrap import ODR_Bootstrap, plot_regression

Prepare calibration data

x_standards = np.array([0.1, 0.5, 1.0, 2.0, 5.0]) # Concentrations y_intensity = np.array([45, 200, 350, 700, 1450]) # Ion counts x_uncertainty = np.array([0.01, 0.05, 0.1, 0.2, 0.5]) # Measurement errors in x y_uncertainty = np.array([5, 20, 35, 60, 120]) # Measurement errors in y

Run ODR bootstrap with 2000 resamples

confidence_data, best_fit_params, points, all_params, subsamples = ODR_Bootstrap( x=x_standards, y=y_intensity, x_err=x_uncertainty, y_err=y_uncertainty, resample_draws=2000, InterceptFit=True, InitialGuess=[250, 10], Confidence_Bound=0.95, LineMax=6, )

Plot the result

fig, ax = plt.subplots(figsize=(8, 5)) plot_regression(confidence_data, datapoints=points, ax=ax, ecolor='lightblue', line_color='darkblue', linewidth=2) ax.set_xlabel('Concentration (ppm)') ax.set_ylabel('Ion Intensity (counts)') ax.set_title('SIMS Calibration Curve with 95% Bootstrap CI') plt.tight_layout() plt.savefig('calibration_curve.png', dpi=150) plt.show()

Access results

print(f"Slope: {best_fit_params[0]:.2f}") print(f"Intercept: {best_fit_params[1]:.2f}")

### Plotting Calibration Estimate Distributions

```python
from odr_bootstrap import plot_Calibration_Estimates
import numpy as np

# Extract bootstrap parameter distributions
all_slopes = np.array([p[0] for p in all_params])
all_intercepts = np.array([p[1] for p in all_params])

# Create synthetic measurement ensemble (for visualization)
fit_params = np.array([[all_slopes.mean(), all_intercepts.mean()]] * 5)
fit_params += np.random.normal(0, [all_slopes.std(), all_intercepts.std()], (5, 2))
fit_error = np.array([[all_slopes.std(), all_intercepts.std()]] * 5)

# Generate plot
fig = plot_Calibration_Estimates(fit_params, fit_error,
                               Title="Calibration Slope & Intercept Distributions")
plt.savefig('calibration_estimates.png', dpi=150)
plt.show()

Module Functions

Core Fitting

• ODR_Linear(x, y, x_err, y_err, intercept=False, InitialGuess=[100, 1])
  Single orthogonal distance regression fit with optional y-intercept. Returns: (fitted_params, param_uncertainties)

• ODR_Linear_Test(x, y, x_err, y_err, ...)
  ODR fit returning full scipy.odr output object for diagnostics.

• Bootstrap_fit(x, y, x_err, y_err, resample_draws, ...)
  Resample data N times and fit ODR model to each resample. Returns: (all_fit_params, resampled_data)

Confidence Intervals

• Eval_Conf(Fit_Param, Confidence_Bound=0.95, LineMax=200, ...)
  Compute confidence intervals from bootstrap parameter distributions. Returns: DataFrame with confidence bounds indexed by x-values.

• ODR_Bootstrap(...)
  Convenience wrapper combining Bootstrap_fit + Eval_Conf in one call.

Statistics

• gauss_agv_err(concentrations, errors, ...)
  Aggregate multiple normal distributions into single KDE estimate. Returns: (distribution_dict, statistics_dict)

Plotting

• plot_regression(confidence_df, datapoints=None, ax=None, ...)
  Plot best-fit line with shaded confidence band.

• plot_datapoints(data, bounds, ax=None, ...)
  Plot probability density curve with summary statistics.

• plot_Calibration_Estimates(fit_params, fit_error, Title=...)
  Side-by-side slope and intercept distribution plots.

Testing

Run the comprehensive test suite:

python -m unittest tests/test_odr_bootstrap.py -v

Or with pytest:

pytest tests/ -v

All 22 tests should pass.

Example Workflow

See examples/example.py for a complete working example:

cd examples
python example.py

This generates:

• calibration_curve.png - Fitted line with confidence band
• calibration_estimates.png - Bootstrap parameter distributions

Recent Updates (April 2025)

• ✅ Fixed zero-intercept ODR fits with proper scipy.odr parameter wrapping
• ✅ Updated deprecated np.trapz API to np.trapezoid (scipy 1.15+ compatible)
• ✅ Added comprehensive NumPy-style docstrings to all functions
• ✅ Created 22 unit tests with 100% pass rate
• ✅ Generated runnable example workflow

API Reference

Full documentation is available in function docstrings:

from odr_bootstrap import ODR_Bootstrap
help(ODR_Bootstrap)

Requirements

• Python >= 3.12
• numpy >= 2.2.4
• scipy >= 1.15.2
• pandas >= 2.2.3
• matplotlib >= 3.10.1

License

MIT License - See LICENSE file for details.

Citation

If you use this package in research, please cite:

@software{towbin2025odr,
  title={ODR Bootstrap: Orthogonal Distance Regression with Bootstrap Resampling},
  author={Towbin, Henry},
  year={2025},
  url={https://github.com/whtowbin/odr-bootstrap}
}

Contributing

Contributions welcome! Please open an issue or submit a pull request.

Acknowledgments

Developed at Caltech for SIMS calibration analysis workflows.

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Status: Beta (0.1.0) | Last Updated: April 2025