ABC model selection for spatial extremes models applied to South Australian maximum temperature data

Discrimination between Gaussian process models: active learning and static constructions

The paper covers the design and analysis of experiments to discriminate between two Gaussian process models with different covariance kernels, such as those widely used in computer experiments, kriging, sensor location and machine learning. Two frameworks are considered. First, we study sequential constructions, where successive design (observation) points are selected, either as additional points to an existing design or from the beginning of observation. The selection relies on the maximisation of the difference between the symmetric Kullback Leibler divergences for the two models, which depends on the observations, or on the mean squared error of both models, which does not. Then, we consider static criteria, such as the familiar log-likelihood ratios and the Fréchet distance between the covariance functions of the two models. Other distance-based criteria, simpler to compute than previous ones, are also introduced, for which, considering the framework of approximate design, a necessary condition for the optimality of a design measure is provided. The paper includes a study of the mathematical links between different criteria and numerical illustrations are provided.

Optimal Bayesian design for model discrimination via classification

Performing optimal Bayesian design for discriminating between competing models is computationally intensive as it involves estimating posterior model probabilities for thousands of simulated data sets. This issue is compounded further when the likelihood functions for the rival models are computationally expensive. A new approach using supervised classification methods is developed to perform Bayesian optimal model discrimination design. This approach requires considerably fewer simulations from the candidate models than previous approaches using approximate Bayesian computation. Further, it is easy to assess the performance of the optimal design through the misclassification error rate. The approach is particularly useful in the presence of models with intractable likelihoods but can also provide computational advantages when the likelihoods are manageable.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11222-022-10078-2.