Bayesian Hierarchical Invariant Prediction (BHIP) proposes a method to reformulate Invariant Causal Prediction (ICP) from the perspective of hierarchical Bayes. It improves computational scalability for more predictors than ICP by explicitly testing the invariance of causal mechanisms in heterogeneous data by leveraging the hierarchical structure. Furthermore, BHIP can use prior information due to its Bayesian property. In this paper, we test two sparsity inducing priors, horseshoe and spike-and-slab, to identify causal features more reliably. We demonstrate its potential as an alternative inference method to ICP by testing BHIP on synthetic and real data.
