The project explored methods of likelihood-free inference and prediction for systems where the underlying dynamics are unknown. The proposed method uses multi-task Bayesian Optimization for inference and Bayesian Linear Auto-Regression for prediction of the underlying parameters. The method was experimented with several toy simulators and two models from human behavioral research. The experiments were implemented by augmenting the ELFI library with multi-task Gaussian Process and Bayesian optimization from GPyTorch and BoTorch.