Sampling in Constrained Space: Efficient Estimation of Model Evidence under Equality and Inequality Constraints

Many scientific theories imply equality and inequality constraints on the statistical model underlying the observed data. Incorporating such constraints into hypothesis testing increases the efficiency and precision of inference. However, existing tools of testing such hypotheses are computationally expensive and do not scale well to complex sets of constraints. Here, we introduce Sampling in Constrained Space (SICS), a highly general approach for performing Bayesian hypothesis testing on constrained models. Through a simple reparameterization, SICS allows the efficient sampling of the posterior distribution from those sections of the parameter space that fulfill all constraints. This, in turn, enables estimating the marginal likelihood under the constrained model, through established algorithms such as bridge sampling. We demonstrate the versatility of SICS by analyzing a learning task dataset using constrained reinforcement learning models, from both a single-level and hierarchical perspective. Our results show that SICS outperforms previous approaches in terms of precision and efficiency. By providing guidelines on its application, we hope to make SICS an integral part of scientists' inferential toolkit.