Minuit was designed to optimize statistical cost functions, for maximum-likelihood and least-squares fits. It provides the best-fit parameters and error estimates from likelihood profile analysis.

The iminuit package brings additional features:

Builtin cost functions for statistical fits to N-dimensional data
- Unbinned and binned maximum-likelihood + extended versions
- Template fits with error propagation <https://doi.org/10.1140/epjc/s10052-022-11019-z>_
- Least-squares (optionally robust to outliers)
- Gaussian penalty terms for parameters
- Cost functions can be combined by adding them: total_cost = cost_1 + cost_2
- Visualization of the fit in Jupyter notebooks
Support for SciPy minimizers as alternatives to Minuit's MIGRAD algorithm (optional)
Support for Numba accelerated functions (optional)

Minimal dependencies

iminuit is promised to remain a lean package which only depends on numpy, but additional features are enabled if the following optional packages are installed.

numba: Cost functions are partially JIT-compiled if numba is installed.
matplotlib: Visualization of fitted model for builtin cost functions
ipywidgets: Interactive fitting, see example below (also requires matplotlib)
scipy: Compute Minos intervals for arbitrary confidence levels
unicodeitplus: Render names of model parameters in simple LaTeX as Unicode

Documentation

Checkout our large and comprehensive list of tutorials_ that take you all the way from beginner to power user. For help and how-to questions, please use the discussions_ on GitHub or gitter_.

Lecture by Glen Cowan

In the exercises to his lecture for the KMISchool 2022 <https://github.com/KMISchool2022>_, Glen Cowan shows how to solve statistical problems in Python with iminuit. You can find the lectures and exercises on the Github page, which covers both frequentist and Bayesian methods.

Glen Cowan <https://scholar.google.com/citations?hl=en&user=ljQwt8QAAAAJ&view_op=list_works>_ is a known for his papers and international lectures on statistics in particle physics, as a member of the Particle Data Group, and as author of the popular book Statistical Data Analysis <https://www.pp.rhul.ac.uk/~cowan/sda/>_.

In a nutshell

iminuit can be used with a user-provided cost functions in form of a negative log-likelihood function or least-squares function. Standard functions are included in iminuit.cost, so you don't have to write them yourself. The following example shows how to perform an unbinned maximum likelihood fit.

.. code:: python

import numpy as np
from iminuit import Minuit
from iminuit.cost import UnbinnedNLL
from scipy.stats import norm

x = norm.rvs(size=1000, random_state=1)

def pdf(x, mu, sigma):
    return norm.pdf(x, mu, sigma)

# Negative unbinned log-likelihood, you can write your own
cost = UnbinnedNLL(x, pdf)

m = Minuit(cost, mu=0, sigma=1)
m.limits["sigma"] = (0, np.inf)
m.migrad()  # find minimum
m.hesse()   # compute uncertainties

.. image:: doc/_static/demo_output.png :alt: Output of the demo in a Jupyter notebook

Interactive fitting

iminuit optionally supports an interactive fitting mode in Jupyter notebooks.

.. image:: doc/_static/interactive_demo.gif :alt: Animated demo of an interactive fit in a Jupyter notebook

High performance when combined with numba

When iminuit is used with cost functions that are JIT-compiled with numba_ (JIT-compiled pdfs are provided by numba_stats_ ), the speed is comparable to RooFit_ with the fastest backend. numba_ with auto-parallelization is considerably faster than the parallel computation in RooFit_.

.. image:: doc/_static/roofit_vs_iminuit+numba.svg

More information about this benchmark is given in the Benchmark section of the documentation <https://scikit-hep.org/iminuit/benchmark.html>_.

Citation

If you use iminuit in a scientific work, please cite us. A generic BibTeX entry is::

@article{iminuit,
  author={Hans Dembinski and Piti Ongmongkolkul et al.},
  title={scikit-hep/iminuit},
  DOI={10.5281/zenodo.3949207},
  publisher={Zenodo},
  year={2020},
  month={Dec},
  url={https://doi.org/10.5281/zenodo.3949207}
}

The DOI and URL in this entry point always to the latest release of iminuit. You can also cite the actual release that you used, please follow the Zenodo link <https://doi.org/10.5281/zenodo.3949207>_, which offers entries for common bibliography formats for all iminuit releases.

The recommended scientific reference for the MINUIT algorithms is::

@article{James:1975dr,
    author = "James, F. and Roos, M.",
    title = "{Minuit: A System for Function Minimization and Analysis of the Parameter Errors and Correlations}",
    reportNumber = "CERN-DD-75-20",
    doi = "10.1016/0010-4655(75)90039-9",
    journal = "Comput. Phys. Commun.",
    volume = "10",
    pages = "343--367",
    year = "1975"
}

Partner projects

numba_stats_ provides faster implementations of probability density functions than scipy, and a few specific ones used in particle physics that are not in scipy.
boost-histogram_ from Scikit-HEP provides fast generalized histograms that you can use with the builtin cost functions.
jacobi_ provides a robust, fast, and accurate calculation of the Jacobi matrix of any transformation function and building a function for generic error propagation.

Versions

The 2.x series has introduced breaking interfaces changes with respect to the 1.x series. There are no plans to introduce further breaking changes.

All interface changes from 1.x to 2.x are documented in the changelog_ with recommendations how to upgrade. To keep old scripts running, pin your major iminuit version to <2: the command pip install 'iminuit<2' installs the 1.x series.

.. _changelog: https://scikit-hep.org/iminuit/changelog.html .. _tutorials: https://scikit-hep.org/iminuit/tutorials.html .. _discussions: https://github.com/scikit-hep/iminuit/discussions .. _gitter: https://gitter.im/Scikit-HEP/iminuit .. _jacobi: https://github.com/hdembinski/jacobi .. _numba_stats: https://github.com/HDembinski/numba-stats .. _boost-histogram: https://github.com/scikit-hep/boost-histogram .. _numba: https://numba.pydata.org .. _RooFit: https://root.cern/manual/roofit/

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