Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of “axis designs” outperforms Latin hypercubes in terms of the IMSE criterion.

Using scenario tree modelling for targeted herd sampling to substantiate freedom from disease

BACKGROUND: In order to optimise the cost-effectiveness of active surveillance to substantiate freedom from disease, a new approach using targeted sampling of farms was developed and applied on the example of infectious bovine rhinotracheitis (IBR) and enzootic bovine leucosis (EBL) in Switzerland. Relevant risk factors (RF) for the introduction of IBR and EBL into Swiss cattle farms were identified and their relative risks defined based on literature review and expert opinions. A quantitative model based on the scenario tree method was subsequently used to calculate the required sample size of a targeted sampling approach (TS) for a given sensitivity. We compared the sample size with that of a stratified random sample (sRS) with regard to efficiency. RESULTS: The required sample sizes to substantiate disease freedom were 1,241 farms for IBR and 1,750 farms for EBL to detect 0.2% herd prevalence with 99% sensitivity. Using conventional sRS, the required sample sizes were 2,259 farms for IBR and 2,243 for EBL. Considering the additional administrative expenses required for the planning of TS, the risk-based approach was still more cost-effective than a sRS (40% reduction on the full survey costs for IBR and 8% for EBL) due to the considerable reduction in sample size. CONCLUSIONS: As the model depends on RF selected through literature review and was parameterised with values estimated by experts, it is subject to some degree of uncertainty. Nevertheless, this approach provides the veterinary authorities with a promising tool for future cost-effective sampling designs.