Essential and incidental measurement error: Bayesian estimation and inference when sample measurements are random-variable-valued

基本和偶然测量误差：样本测量为随机变量值时的贝叶斯估计和推断

• 批准号: RGPIN-2021-04357
• 负责人: Kroc, Edward
• 金额: $ 1.31万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=751499
• 关键词: Essential; incidental; measurement; error; Bayesian

BACKGROUND: This Discovery Grant will support the long term goal of further developing a theory of random-variable-valued measurements (RVVMs), a novel generalization of classical and Berkson measurement error modelling that I have been developing for the past 5 years as a postdoctoral researcher and new Assistant Professor, and applying this theory to solve modern problems in ecology and conservation of species-at-risk. Traditional notions of measurement error treat the problem as one of misclassification or mismeasurement. However, there are often instances that arise in an applied data collection system when sample measurements do not generate simply sample instantiations of a real-valued random variable. Instead, we may find ourselves in a situation where the measurement process generates sample data that are themselves new random variables that describe the chance of observing a particular value, or range of values, for the target phenomenon in question on each sample draw. OBJECTIVES: The most pertinent theoretical matters to be addressed over the duration of the grant are: (1) A characterization of different calibration conditions that generalize other popular measurement error models to the RVVM setting; (2) A study of maximum likelihood estimators derived from RVVM sample data; (3) Generalization to an operator theoretic framework and connections to the mathematical physics approach of observables as linear operators on a Hilbert space. In addition, the following applications of the RVVM framework will be further developed: (1) Easy R implementation of multinomial-valued measurements and protocols for population modelling and data collection in bird-banding operations; (2) Easy R implementation of multinomial-valued and normal-valued measurements for citizen-science-sourced population data of avian species via eBird and related platforms; (3) Adaptation of RVVM framework to spatio-temporal modelling scenarios for application to unsure nest identification of difficult-to-survey urban-nesting avian species; (4) Integration of RVVM framework into automated object classification from aerial imagery of seabird colonies. IMPACT: This work's theoretical developments can improve the scientific understanding of measurement in the mathematical, statistical, and decision sciences, while its applications can have immediate impact in the ecological and environmental sciences, particularly with regards to solving real and difficult problems related to conservation of species-at-risk. A variety of theoretical and applied papers and technical presentations will result from this work, as well as the creation of several R software packages for applied practitioners to implement these methods in various research scenarios. This program will train 2 undergraduates, 4 MSc and 2 PhD students in the mathematical, statistical, and ecological sciences and prepare them for careers in data science, statistics, ecology, and conservation.

背景技术背景：这项发现补助金将支持进一步发展随机变量值测量理论（RVVMs）的长期目标，这是我作为博士后研究员和新助理教授在过去5年中一直在开发的经典和Berkson测量误差模型的新概括，并应用该理论解决生态学和濒危物种保护的现代问题。传统的测量误差概念将问题视为错误分类或错误测量。然而，在应用的数据收集系统中，当样本测量不生成实值随机变量的简单样本实例时，经常会出现这样的情况。相反，我们可能会发现自己处于这样一种情况，即测量过程生成的样本数据本身就是新的随机变量，这些变量描述了在每次抽样时观察到目标现象的特定值或值范围的机会。 目的：最相关的理论问题，以解决在资助期间：（1）不同的校准条件，推广其他流行的测量误差模型的RVVM设置的特征：（2）来自RVVM样本数据的最大似然估计的研究;（三）算子理论框架的推广和作为希尔伯特上线性算子的可观测量的数学物理方法的联系空间 此外，将进一步开发RVVM框架的以下应用：（1）Easy R实现多项值测量和协议，用于鸟类环志操作中的种群建模和数据收集;（2）Easy R通过eBird和相关平台实现多项值和正态值测量，用于公民科学来源的鸟类种群数据;（3）将RVVM框架应用于时空模拟场景，以应用于难以调查的城市筑巢鸟类物种的不确定巢识别;（4）将RVVM框架集成到海鸟群体航空图像的自动目标分类中。影响：这项工作的理论发展可以提高测量的数学，统计和决策科学的科学理解，而其应用可以在生态和环境科学，特别是在解决真实的和困难的问题有关的保护物种的风险有直接的影响。这项工作将产生各种理论和应用论文和技术演示，以及为应用实践者创建几个R软件包，以在各种研究场景中实现这些方法。该计划将培养2名本科生，4名硕士和2名博士生在数学，统计和生态科学，并准备他们在数据科学，统计，生态和保护的职业生涯。