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Survey sampling plays an important role in the efficient allocation and management of resources. The essence of survey sampling lies in acquiring a sample of data points from a population and subsequently using this sample to estimate the population parameters of the targeted response variable, such as environmental-related metrics or other pertinent factors. Practical limitations imposed on survey sampling necessitate prudent consideration of the number of samples attainable from the study areas, given the constraints of a fixed budget. To this end, researchers are compelled to employ sampling designs that optimize sample allocations to the best of their ability. Generally, probability sampling serves as the preferred method, ensuring an unbiased estimation of population parameters. Evaluating the efficiency of estimators involves assessing their variances and benchmarking them against alternative baseline approaches, such as simple random sampling. In this study, we propose a novel model-assisted unbiased probability sampling method that leverages Bayesian optimization for the determination of sampling designs. As a result, this approach can yield in estimators with more efficient variance outcomes compared to the conventional estimators such as the Horvitz-Thompson. Furthermore, we test the proposed method in a simulation study using an empirical dataset covering plot-level tree volume from central Finland. The results demonstrate statistically significant improved performance for the proposed method when compared to the baseline., Comment: 16 pages, 1 figure, 2 tables

In large-area forest inventories a trade-off between the amount of data to be sampled and the costs of collecting the data is necessary. It is not always possible to have a very large data sample when dealing with sampling-based inventories. It is therefore necessary to optimize the sampling design in order to achieve optimal population parameter estimation. On the contrary, the availability of remote sensing (RS) data correlated with the forest inventory variables is usually much higher. The combination of RS and the sampled field measurement data is often used for improving the forest inventory parameter estimation. In addition, it is also reasonable to study the utilization of RS data in inventory sampling, which can further improve the estimation of forest variables. In this study, we propose a data sampling method based on Bayesian optimization which uses RS data in forest inventory sample selection. The presented method applies the learned functional relationship between the RS and inventory data in new sampling decisions. We evaluate our method by conducting simulated sampling experiments with both synthetic data and measured data from the Aland region in Finland. The proposed method is benchmarked against two baseline methods: simple random sampling and the local pivotal method. The results of the simulated experiments show the best results in terms of MSE values for the proposed method when the functional relationship between RS and inventory data is correctly learned from the available training data., Comment: 36 pages, 8 figures, 3 tables