Cross-validation-based sequential design for stochastic models

Complex numerical models are increasingly being used in healthcare and epidemiology. To represent the complex features, modellers often make the decision to include stochastic behaviour where repeated runs of the model with identical inputs produce different outputs. When computational constraints limit the number of model runs and replications, heteroscedastic Gaussian processes can be used as a fast surrogate, allowing for efficient emulation of varying noise levels across the input space. The accuracy of any emulator is greatly dependent on the design of the training data, where sequential design algorithms increase the number of design points iteratively based on predefined criteria. For stochastic models, the design problem is more challenging due to the possibility of replicates at design points. This article develops a new sequential design method for stochastic models which scales well in high-dimensional input spaces. We build upon an existing method for deterministic models using an expected squared leave-one-out error criterion that balances exploration and replication. We compare our approach with existing sequential design methods as well as applying it to an agent-based model and a COVID-19 model. Results demonstrate that the proposed method performs well in noisy environments, offering a scalable alternative to existing methods.This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 2)'.