Skip to main content

Fit and compare complex models reliably and rapidly. Advanced Nested Sampling.

Project description


Fit and compare complex models reliably and rapidly with advanced sampling techniques. Documentation Status Github repository Software paper

Correctness. Speed. Ease of use. 🦔


When scientific models are compared to data, two tasks are important: 1) contraining the model parameters and 2) comparing the model to other models. Different techniques have been developed to explore model parameter spaces. This package implements a Monte Carlo technique called nested sampling.

Nested sampling allows Bayesian inference on arbitrary user-defined likelihoods. In particular, posterior probability distributions on model parameters are constructed, and the marginal likelihood (“evidence”) Z is computed. The former can be used to describe the parameter constraints of the data, the latter can be used for model comparison (via Bayes factors) as a measure of the prediction parsimony of a model.

In the last decade, multiple variants of nested sampling have been developed. These differ in how nested sampling finds better and better fits while respecting the priors (constrained likelihood prior sampling techniques), and whether it is allowed to go back to worse fits and explore the parameter space more.

This package develops novel, advanced techniques for both (See How it works). They are especially remarkable for being free of tuning parameters and theoretically justified. Beyond that, UltraNest has support for Big Data sets and high-performance computing applications.

UltraNest is intended for fitting complex physical models with slow likelihood evaluations, with one to hundreds of parameters. UltraNest intends to replace heuristic methods like multi-ellipsoid nested sampling and dynamic nested sampling with more rigorous methods. UltraNest also attempts to provide feature parity compared to other packages (such as MultiNest).

You can help by testing UltraNest and reporting issues. Code contributions are welcome. See the Contributing page.


  • Pythonic

    • pip and conda installable

    • Easy to program for: Sanity checks with meaningful errors

    • Can control the run programmatically and check status

    • Reasonable defaults, but customizable

    • Thoroughly tested with many unit and integration tests

    • NEW: supports likelihood functions written in Python, C, C++, Fortran, Julia and R

  • Robust exploration easily handles:

    • Degenerate parameter spaces such as bananas or tight correlations

    • Multiple modes/solutions in the parameter space

    • Robust, parameter-free MLFriends algorithm (metric learning RadFriends, Buchner+14,+19), with new improvements (region follows new live points, clustering improves metric iteratively, NEW in v4.0: refined local metric).

    • High-dimensional problems with hit-and-run sampling

    • Wrapped/circular parameters, derived parameters

    • Fast-slow parameters

  • Lightweight and fast

  • Advanced visualisation and crash recovery:

    • Live view of the exploration for Jupyter notebooks and terminals

    • Publication-ready visualisations

    • Corner plots, run and parameter exploration diagnostic plots

    • Checkpointing and resuming, even with different number of live points

    • Warm-start: resume from modified data / model

  • strategic nested sampling

    • can vary (increase) number of live points (akin to dynamic nested sampling, but with different targets)

    • can sample clusters optimally (e.g., at least 50 points per cluster/mode/solution)

    • can target minimizing parameter estimation uncertainties

    • can target a desired evidence uncertainty threshold

    • can target a desired number of effective samples

    • or any combination of the above

    • Robust ln(Z) uncertainties by bootstrapping live points.


Get started!

Read the full documentation with tutorials at:

API Reference:.

Code repository:


How to cite UltraNest.

GPLv3 (see LICENCE file). If you require another license, please contact me.

The cute hedgehog icon was made by Freepik. It symbolises UltraNest’s approach of carefully walking up a likelihood, ready to defend against any encountered danger.

Release Notes

4.2.0 (2024-02-15)

  • new ultranest.mlfriends.LocalAffineLayer for metric learning, set as default (see issue 124)

  • add Highest Density Interval function (ultranest.plot.highest_density_interval_from_samples)

  • corner plot style with higher signal-to-ink ratio.

  • bug fixes in popstepsampler

4.1.0 (2024-02-15)

  • add number of steps calibrator ultranest.calibrator.ReactiveNestedCalibrator

  • add relative jump distance diagnostic for step samplers

  • make population step samplers more consistent with other step samplers

4.0.0 (2024-02-15)

  • new ultranest.mlfriends.MaxPrincipleGapAffineLayer for metric learning, set as default

3.6.5 (2023-07-18)

3.6.0 (2023-06-22)

  • add PopulationRandomWalkSampler: vectorized Gaussian random walks for GPU/JAX-powered likelihoods

  • limit initial widening to escape plateau (issue #81)

3.5.0 (2022-09-05)

  • add hot-resume: resume from a similar fit (with different data)

  • fix post_summary.csv column order

  • fix build handling for non-pip systems (pyproject.toml)

  • more efficient handling of categorical variables

3.4.0 (2022-04-05)

  • add differential evolution proposal for slice sampling, recommend it

  • fix revert of step sampler when run out of constraint, in MPI

  • add SimpleRegion: axis-aligned ellipsoidal for very high-d.

3.3.3 (2021-09-17)

  • pretty marginal posterior plot to stdout

  • avoid non-terminations when logzerr cannot be reached

  • add RobustEllipsoidRegion: ellipsoidal without MLFriends for high-d.

  • add WrappingEllipsoid: for additional rejection.

  • bug fixes on rank order test

  • add resume-similar

  • modular step samplers

3.0.0 (2020-10-03)

  • Accelerated Hit-and-Run Sampler added

  • Support for other languages (C, C++, Julia, Fortran) added

  • Insertion order test added

  • Warm-start added

  • Rejection sampling with transformed ellipsoid added

2.2.0 (2020-02-07)

  • allow reading UltraNest outputs without ReactiveNestedSampler instance

2.1.0 (2020-02-07)

  • adaptive number of steps for slice and hit-and-run samplers.

2.0.0 (2019-10-03)

  • First release.

1.0.0 (2014)

  • A simpler version referenced in Buchner et al. (2014), combining RadFriends with an optional Metropolis-Hastings proposal.

Project details

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

ultranest-4.3.1.tar.gz (2.7 MB view hashes)

Uploaded Source

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page