sbi: Simulation-Based Inference

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sbi is a Python package for simulation-based inference, designed to meet the needs of both researchers and practitioners. Whether you need fine-grained control or an easy-to-use interface, sbi has you covered.

With sbi, you can perform parameter inference using Bayesian inference: Given a simulator that models a real-world process, SBI estimates the full posterior distribution over the simulator’s parameters based on observed data. This distribution indicates the most likely parameter values while additionally quantifying uncertainty and revealing potential interactions between parameters.

Key Features of sbi

sbi offers a blend of flexibility and ease of use:

• Low-Level Interfaces: For those who require maximum control over the inference process, sbi provides low-level interfaces that allow you to fine-tune many aspects of your workflow.
• High-Level Interfaces: If you prefer simplicity and efficiency, sbi also offers high-level interfaces that enable quick and easy implementation of complex inference tasks.

In addition, sbi supports a wide range of state-of-the-art inference algorithms (see below for a list of implemented methods):

• Amortized Methods: These methods enable the reuse of posterior estimators across multiple observations without the need to retrain.
• Sequential Methods: These methods focus on individual observations, optimizing the number of simulations required.

Beyond inference, sbi also provides:

• Validation Tools: Built-in methods to validate and verify the accuracy of your inferred posteriors.
• Plotting and Analysis Tools: Comprehensive functions for visualizing and analyzing results, helping you interpret the posterior distributions with ease.

Getting started with sbi is straightforward, requiring only a few lines of code:

```python from sbi.inference import NPE

Given: parameters theta and corresponding simulations x

inference = NPE(prior=prior) inference.appendsimulations(theta, x).train() posterior = inference.buildposterior() ```

Installation

sbi requires Python 3.10 or higher. While a GPU isn't necessary, it can improve performance in some cases. We recommend using a virtual environment with conda for an easy setup.

If conda is installed on the system, an environment for installing sbi can be created as follows:

bash conda create -n sbi_env python=3.10 && conda activate sbi_env

From PyPI

To install sbi from PyPI run

bash python -m pip install sbi

From conda-forge

To install and add sbi to a project with pixi, from the project directory run

bash pixi add sbi

and to install into a particular conda environment with conda, in the activated environment run

bash conda install --channel conda-forge sbi

If uv is installed on the system, an environment for installing sbi can be created as follows:

bash uv venv -p 3.10

Then activate the virtual enviroment by running:

• For macOS or Linux users bash source .venv/bin/activate

• For Windows users bash .venv\Scripts\activate

To install sbi run

bash uv add sbi

Testing the installation

Open a Python prompt and run

python from sbi.examples.minimal import simple posterior = simple() print(posterior)

Tutorials

If you're new to sbi, we recommend starting with our Getting Started tutorial.

You can also access and run these tutorials directly in your browser by opening Codespace. To do so, click the green “Code” button on the GitHub repository and select “Open with Codespaces.” This provides a fully functional environment where you can explore sbi through Jupyter notebooks.

Inference Algorithms

The following inference algorithms are currently available. You can find instructions on how to run each of these methods here.

Neural Posterior Estimation: amortized (NPE) and sequential (SNPE)

• (S)NPE_A (including amortized single-round NPE) from Papamakarios G and Murray I Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation (NeurIPS 2016).

• (S)NPE_B from Lueckmann JM, Goncalves P, Bassetto G, Öcal K, Nonnenmacher M, and Macke J Flexible statistical inference for mechanistic models of neural dynamics (NeurIPS 2017).

• (S)NPE_C or APT from Greenberg D, Nonnenmacher M, and Macke J Automatic Posterior Transformation for likelihood-free inference (ICML 2019).

• TSNPE from Deistler M, Goncalves P, and Macke J Truncated proposals for scalable and hassle-free simulation-based inference (NeurIPS 2022).

• FMPE from Wildberger, J., Dax, M., Buchholz, S., Green, S., Macke, J. H., & Schölkopf, B. Flow matching for scalable simulation-based inference. (NeurIPS 2023).

• NPSE from Geffner, T., Papamakarios, G., & Mnih, A. Compositional score modeling for simulation-based inference. (ICML 2023)

Neural Likelihood Estimation: amortized (NLE) and sequential (SNLE)

• (S)NLE or just SNL from Papamakarios G, Sterrat DC and Murray I Sequential Neural Likelihood (AISTATS 2019).

Neural Ratio Estimation: amortized (NRE) and sequential (SNRE)

• (S)NRE_A or AALR from Hermans J, Begy V, and Louppe G. Likelihood-free Inference with Amortized Approximate Likelihood Ratios (ICML 2020).

• (S)NRE_B or SRE from Durkan C, Murray I, and Papamakarios G. On Contrastive Learning for Likelihood-free Inference (ICML 2020).

• (S)NRE_C or NRE-C from Miller BK, Weniger C, Forré P. Contrastive Neural Ratio Estimation (NeurIPS 2022).

• BNRE from Delaunoy A, Hermans J, Rozet F, Wehenkel A, and Louppe G. Towards Reliable Simulation-Based Inference with Balanced Neural Ratio Estimation (NeurIPS 2022).

Neural Variational Inference, amortized (NVI) and sequential (SNVI)

• SNVI from Glöckler M, Deistler M, Macke J, Variational methods for simulation-based inference (ICLR 2022).

Mixed Neural Likelihood Estimation (MNLE)

• MNLE from Boelts J, Lueckmann JM, Gao R, Macke J, Flexible and efficient simulation-based inference for models of decision-making (eLife 2022).

Feedback and Contributions

We welcome any feedback on how sbi is working for your inference problems (see Discussions) and are happy to receive bug reports, pull requests, and other feedback (see contribute). We wish to maintain a positive and respectful community; please read our Code of Conduct.

Acknowledgments

sbi is the successor (using PyTorch) of the delfi package. It started as a fork of Conor M. Durkan's lfi. sbi runs as a community project. See also credits.

Support

sbi has been supported by the German Federal Ministry of Education and Research (BMBF) through project ADIMEM (FKZ 01IS18052 A-D), project SiMaLeSAM (FKZ 01IS21055A) and the Tübingen AI Center (FKZ 01IS18039A). Since 2024, sbi is supported by the appliedAI Institute for Europe, and by NumFOCUS.

License

Apache License Version 2.0 (Apache-2.0)

Citation

The sbi package has grown and improved significantly since its initial release, with contributions from a large and diverse community. To reflect these developments and the expanded functionality, we published an updated JOSS paper. We encourage you to cite this newer version as the primary reference:

latex @article{BoeltsDeistler_sbi_2025, doi = {10.21105/joss.07754}, url = {https://doi.org/10.21105/joss.07754}, year = {2025}, publisher = {The Open Journal}, volume = {10}, number = {108}, pages = {7754}, author = {Jan Boelts and Michael Deistler and Manuel Gloeckler and Álvaro Tejero-Cantero and Jan-Matthis Lueckmann and Guy Moss and Peter Steinbach and Thomas Moreau and Fabio Muratore and Julia Linhart and Conor Durkan and Julius Vetter and Benjamin Kurt Miller and Maternus Herold and Abolfazl Ziaeemehr and Matthijs Pals and Theo Gruner and Sebastian Bischoff and Nastya Krouglova and Richard Gao and Janne K. Lappalainen and Bálint Mucsányi and Felix Pei and Auguste Schulz and Zinovia Stefanidi and Pedro Rodrigues and Cornelius Schröder and Faried Abu Zaid and Jonas Beck and Jaivardhan Kapoor and David S. Greenberg and Pedro J. Gonçalves and Jakob H. Macke}, title = {sbi reloaded: a toolkit for simulation-based inference workflows}, journal = {Journal of Open Source Software} }

This updated paper, with its expanded author list, reflects the broader community contributions and the package's enhanced capabilities in releases 0.23.0 and later.

If you are using a version of sbi prior to 0.23.0, please cite the original sbi software paper:

latex @article{tejero-cantero2020sbi, doi = {10.21105/joss.02505}, url = {https://doi.org/10.21105/joss.02505}, year = {2020}, publisher = {The Open Journal}, volume = {5}, number = {52}, pages = {2505}, author = {Alvaro Tejero-Cantero and Jan Boelts and Michael Deistler and Jan-Matthis Lueckmann and Conor Durkan and Pedro J. Gonçalves and David S. Greenberg and Jakob H. Macke}, title = {sbi: A toolkit for simulation-based inference}, journal = {Journal of Open Source Software} }

Regardless of which software paper you cite, please also remember to cite the original research articles describing the specific sbi-algorithm(s) you are using.

Specific releases of sbi are also citable via Zenodo, where we generate a new software DOI for each release.