ELFI: Engine for Likelihood-Free Inference

We introduce an Engine for Likelihood-Free Inference (ELFI), a software package for approximate Bayesian inference that can be used when the likelihood function is difficult to evaluate or unknown, but a generative simulator model exists. The software is in Python, and its modular library design emphasizes both ease-of-use and expandability, allowing arbitrary user-defined simulators and implementation of new inference methods with minimal effort. Probabilistic inference models can be represented intuitively as graphs, and users can execute the inference in a computational environment best suited for their needs, from single laptops to cluster computers. The whole inference pipeline is automatically parallelized, and intermediate results may be stored to disk for later use. The package includes implementations of some of the most advanced likelihood-free inference techniques. One example of these is BOLFI, which estimates the discrepancy function using Gaussian processes and uses Bayesian optimization for parameter search, which has recently been shown to accelerate likelihood-free inference up to several orders of magnitude.