  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.
