MCUP

Monte Carlo Uncertainty Propagation — a Python library for regression with measurement errors.

MCUP provides three sklearn-like estimators that correctly propagate x and y measurement uncertainties into parameter confidence intervals.

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Estimators

Estimator	Use when	Error model
WeightedRegressor	Only y has measurement errors	Σ (y - f(x))² / σ_y²
XYWeightedRegressor	Both x and y have errors	Combined variance via error propagation
DemingRegressor	Both x and y have errors (exact)	Joint optimisation over parameters + latent true x

Each estimator supports two solvers via method:

• "analytical" — weighted least squares + (J^T W J)^{-1} covariance (fast)
• "mc" — Monte Carlo sampling with weighted objective + Welford covariance (robust for nonlinear models)

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Installing

python3 -m pip install mcup

Dev version:

python3 -m pip install git+https://github.com/detrin/MCUP.git#egg=mcup

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Quick Example

import numpy as np
from mcup import WeightedRegressor

def line(x, p):
    return p[0] + p[1] * x

x = np.linspace(0, 10, 30)
y = line(x, [1.0, 2.0]) + np.random.normal(0, 0.5, 30)
y_err = 0.5 * np.ones(30)

est = WeightedRegressor(line, method="analytical")
est.fit(x, y, y_err=y_err, p0=[0.0, 0.0])

print(est.params_)      # [~1.0, ~2.0]
print(est.params_std_)  # parameter uncertainties
print(est.covariance_)  # full covariance matrix

See the Getting Started guide for more examples, or the API Reference for full documentation.