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.

翻译：调查抽样在资源的高效分配与管理中发挥着重要作用。其核心在于从总体中获取数据点样本，并利用该样本估计目标响应变量的总体参数（例如环境相关指标或其他相关因素）。由于实际条件限制，在固定预算约束下，调查抽样必须审慎考虑可从研究区域获取的样本数量。为此，研究人员需要采用能够最大限度优化样本分配的抽样设计。通常，概率抽样是首选方法，可确保总体参数的无偏估计。评估估计量效率需分析其方差，并以此为基准与简单随机抽样等替代方法进行比较。本研究提出了一种新颖的模型辅助无偏概率抽样方法，利用贝叶斯优化确定抽样设计。相较于传统估计量（如霍维茨-汤普森估计量），该方法可显著提升估计量的方差效率。此外，我们利用涵盖芬兰中部地块级林木体积的实证数据集进行模拟研究，验证了所提方法的有效性。结果表明，与基准方法相比，该方法的性能改进具有统计显著性。