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We introduce Julia package ospats+ for optimal sampling design in the context of farm-scale soil carbon auditing. The main difference with package ospats is that ospats+ maximises the expected profit for the farmer, rather than the statistical criterion of estimation precision. The package is written in Julia for speed of computation. Our methodology has been discussed in general terms by de Gruijter et al. (2016), here we go into the computational aspects. Using a grid of predicted carbon content with associated uncertainty, we optimise a stratified random sampling design: number of strata, stratification of the grid, total sample size and sample sizes within strata. The expected profit is maximised on the basis of sequestered carbon price, sampling costs, and a trading parameter that balances farmer's and buyer's risks due to uncertainty of the estimated amount of sequestered carbon. The core of the methodology is optimisation of the stratification by the Ospats method (de Gruijter et al., 2015), an iterative procedure that re-allocates grid points to strata on the basis of pairwise generalised distances between grid points. The distances are a function of the locations, the predictions and the covariances of the prediction errors. We illustrate the use of ospats+ with an application to an Australian farm.
The affiliations of the authors are updated, and a correction in equation 2 is made.