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Inverse binomial sampling for efficient log-likelihood estimation of simulator models
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matlab fixed bug with nll threshold Jan 22, 2020

Inverse binomial sampling (IBS)

What is it

IBS is a technique to obtain unbiased, efficient estimates of the log-likelihood of a model by simulation. [1]

The typical scenario is the case in which you have an implicit model from which you can randomly draw synthetic observations (for a given parameter vector), but cannot evaluate the log-likelihood analytically or numerically. In other words, IBS affords likelihood-based inference for likelihood-free models.


This repository stores basic and advanced implementations and example usages of IBS in various programming languages for users of the method. For the moment, we only have a MATLAB implementation, but we plan to include other ones (e.g., Python).

The code used to produce results in the paper [1] is available in the development repository here.


  1. van Opheusden*, B., Acerbi*, L. & Ma, W.J. (2020). Unbiased and efficient log-likelihood estimation with inverse binomial sampling. arXiv preprint. (* equal contribution) (preprint on arXiv)

You can cite IBS in your work with something along the lines of

We estimated the log-likelihood using inverse binomial sampling (IBS; van Opheusden et al., 2019), a technique that produces unbiased and efficient estimates of the log-likelihood via simulation.

If you use IBS in conjunction with Bayesian Adaptive Direct Search, as recommended in the paper, you could add

We obtained maximum-likelihood estimates of the model parameters via Bayesian Adaptive Direct Search (BADS; Acerbi & Ma, 2017), a hybrid Bayesian optimization algorithm which affords stochastic objective evaluations.

  1. Acerbi, L. & Ma, W. J. (2017). Practical Bayesian optimization for model fitting with Bayesian Adaptive Direct Search. In Advances in Neural Information Processing Systems 30:1834-1844.

Besides formal citations, you can demonstrate your appreciation for our work in the following ways:

  • Star the IBS repository on GitHub;
  • Follow us on Twitter (Luigi, Bas) for updates about IBS and other projects we are involved with;
  • Tell us about your model-fitting problem and your experience with IBS (positive or negative) at or (putting 'IBS' in the subject of the email).


The IBS code is released under the terms of the MIT License.

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