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.

Sequential experimental design for predator-prey functional response experiments.

Understanding functional response within a predator-prey dynamic is a cornerstone for many quantitative ecological studies. Over the past 60 years, the methodology for modelling functional response has gradually transitioned from the classic mechanistic models to more statistically oriented models. To obtain inferences on these statistical models, a substantial number of experiments need to be conducted. The obvious disadvantages of collecting this volume of data include cost, time and the sacrificing of animals. Therefore, optimally designed experiments are useful as they may reduce the total number of experimental runs required to attain the same statistical results. In this paper, we develop the first sequential experimental design method for predator-prey functional response experiments. To make inferences on the parameters in each of the statistical models we consider, we use sequential Monte Carlo, which is computationally efficient and facilitates convenient estimation of important utility functions. It provides coverage of experimental goals including parameter estimation, model discrimination as well as a combination of these. The results of our simulation study illustrate that for predator-prey functional response experiments sequential design outperforms static design for our experimental goals. R code for implementing the methodology is available via https://github.com/haydenmoffat/sequential_design_for_predator_prey_experiments.

Likelihood-free simulation-based optimal design with an application to spatial extremes.

In this paper we employ a novel method to find the optimal design for problems where the likelihood is not available analytically, but simulation from the likelihood is feasible. To approximate the expected utility we make use of approximate Bayesian computation methods. We detail the approach for a model on spatial extremes, where the goal is to find the optimal design for efficiently estimating the parameters determining the dependence structure. The method is applied to determine the optimal design of weather stations for modeling maximum annual summer temperatures.