Open-source tools for fitting models to data
Find the best-fitting parameters, the full posterior and the model evidence from a small budget of model evaluations, whether each one takes a fraction of a second or several minutes, and even when the likelihood is noisy or only available by simulation. In Python and MATLAB.
PyVBMC learning a banana-shaped posterior, drawn from a real run. Explore it
Start here
“I want the parameters that fit my data best.”
→ PyBADS
Maximum-likelihood and MAP fits, with up to about 20 parameters.
“I want the posterior over my parameters, and to compare models.”
→ PyVBMC
The posterior and the model evidence, best with up to about 10 parameters.
“I can simulate my model, but I can't write down its likelihood.”
→ PyIBS, then PyBADS or PyVBMC
For data with discrete responses.
The tools
Fit your model
Bayesian Adaptive Direct Search: fast, robust optimization for maximum-likelihood and MAP fits when the objective is rough, noisy or slow to evaluate, with up to about 20 parameters.
pip install pybads
Acerbi & Ma, NeurIPS 2017 · Singh & Acerbi, JOSS 2024
Get the posterior and the evidence
Variational Bayesian Monte Carlo: an approximate posterior over your parameters and an estimate of the model evidence, for model comparison, from a small budget of likelihood evaluations, even noisy ones. Best with up to about 10 parameters.
pip install pyvbmc
Docs Python MATLAB A run in 3D
Acerbi, NeurIPS 2018 and NeurIPS 2020 · Huggins, Li, Tobaben, Aarnos & Acerbi, JOSS 2023
When you can only simulate
Inverse binomial sampling: unbiased, efficient estimates of the log-likelihood of models you can simulate but not write down, for data with discrete responses. Pair it with PyBADS or PyVBMC, which are built to handle noisy estimates.
pip install pyibs
van Opheusden, Acerbi & Ma, PLOS Computational Biology 2020
Next wave
In active development
The Amortized Conditioning Engine: one transformer, trained on simulated data, that answers inference and prediction questions in a single forward pass and can take prior information at run time. It is research code in active development, and the start of our next generation of methods. nanoACE is a small, readable implementation with an in-browser playground.
Chang, Loka, Huang, Remes, Kaski & Acerbi, AISTATS 2025
In use
Our tools started in cognitive science and neuroscience, where many of their users still are. They now fit models across the sciences and engineering. A few examples:
Story · Perception
How does the brain decide whether a sight and a sound come from the same thing? A short film about causal inference in perception, and about a study whose models were fitted with BADS.
Help and news
Questions about the tools, or how to use them for your model? Ask in our Discussions forum. New methods are on the way: follow Luigi to hear about releases and papers.
