Data from: Combining statistical inference and decisions in ecology

Statistical decision theory (SDT) is a sub-field of decision theory that formally incorporates statistical investigation into a decision-theoretic framework to account for uncertainties in a decision problem. SDT provides a unifying analysis of three types of information: statistical results from a data set, knowledge of the consequences of potential choices (i.e., loss), and prior beliefs about a system. SDT links the theoretical development of a large body of statistical methods including point estimation, hypothesis testing, and confidence interval estimation. The theory and application of SDT have mainly been developed and published in the fields of mathematics, statistics, operations research, and other decision sciences, but have had limited exposure in ecology. Thus, we provide an introduction to SDT for ecologists and describe its utility for linking the conventionally separate tasks of statistical investigation and decision making in a single framework. We describe the basic framework of both Bayesian and frequentist SDT, its traditional use in statistics, and discuss its application to decision problems that occur in ecology. We demonstrate SDT with two types of decisions: Bayesian point estimation, and an applied management problem of selecting a prescribed fire rotation for managing a grassland bird species. Central to SDT, and decision theory in general, are loss functions. Thus, we also provide basic guidance and references for constructing loss functions for an SDT problem.统计决策理论（Statistical Decision Theory, SDT）是决策理论的一个子领域，它将统计调查正式纳入决策论框架，以应对决策问题中的不确定性。SDT可对三类信息开展统一分析：数据集衍生的统计结果、潜在选择的后果（即损失）的相关知识，以及针对某一系统的先验信念。SDT将包括点估计、假设检验与置信区间估计在内的大量统计方法的理论发展进行了统一关联。其理论与应用主要在数学、统计学、运筹学及其他决策科学领域得到发展与发表，但在生态学领域的应用相对有限。因此，我们面向生态学者介绍统计决策理论，并阐述其在单一框架下整合原本相互独立的统计研究与决策任务的实用价值。我们将介绍贝叶斯与频率学派统计决策理论的基本框架，以及其在统计学中的传统应用，并探讨其在生态学决策问题中的应用。我们通过两类决策场景展示SDT的应用：贝叶斯点估计，以及为管理某一草地鸟类物种而制定规定火烧轮期的实际管理问题。损失函数是统计决策理论乃至一般决策理论的核心，因此我们还为构建SDT问题中的损失函数提供基础指导与参考文献。