The ecological status of lakes is important for understanding an ecosystem's biodiversity as well as for service water quality and policies related to land use and agricultural run-off. If the status is weak, then decisions about management alternatives need to be made. We assess the value of information of lake monitoring in Finland, where lakes are abundant. With reasonable ecological values and restoration costs, the value of information analysis can be compared with the survey's costs. Data are worth gathering if the expected value from the data exceeds the costs. From existing data, we specify a hierarchical Bayesian spatial logistic regression model for the ecological status of lakes. We then rely on functional approximations and Laplace approximations to get closed-form expressions for the value of information of a sampling design. The case study contains thousands of lakes. The combinatorially difficult design problem is to wisely pick the right subset of lakes for data gathering. To solve this optimization problem, we study the performance of various heuristics: greedy forward algorithms, exchange algorithms and Bayesian optimization approaches. The value of information increases quickly when adding lakes to a small design but then flattens out. Good designs are usually composed of lakes that are difficult to manage, while also balancing a variety of covariates and geographic coverage. The designs achieved by forward selection are reasonably good, but we can outperform them with the more nuanced search algorithms. Statistical designs clearly outperform other designs selected according to simpler criteria.

中文翻译：

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用于改进湖泊管理决策的抽样设计方法

湖泊的生态状况对于了解生态系统的生物多样性以及服务水质以及与土地利用和农业径流相关的政策非常重要。如果地位较弱，则需要做出有关管理替代方案的决策。我们评估了湖泊丰富的芬兰湖泊监测信息的价值。有了合理的生态价值和恢复成本，信息分析的价值就可以与调查的成本进行比较。如果数据的预期价值超过成本，那么数据就值得收集。根据现有数据，我们指定了湖泊生态状况的分层贝叶斯空间逻辑回归模型。然后，我们依靠函数近似和拉普拉斯近似来获得抽样设计信息值的封闭式表达式。该案例研究包含数千个湖泊。组合困难的设计问题是明智地选择正确的湖泊子集来收集数据。为了解决这个优化问题，我们研究了各种启发式算法的性能：贪婪前向算法、交换算法和贝叶斯优化方法。当在小型设计中添加湖泊时，信息的价值会迅速增加，但随后就会变平。好的设计通常由难以管理的湖泊组成，同时还要平衡各种协变量和地理覆盖范围。通过前向选择实现的设计相当不错，但我们可以通过更细致的搜索算法超越它们。统计设计明显优于根据更简单的标准选择的其他设计。