Chemical measurement methods are designed to promote accurate knowledge of a measurand or system. As such, these methods often allow elicitation of latent sources of variability and correlation in experimental data. They typically implement measurement equations that support quantification of effects associated with calibration standards and other known or observed parametric variables. Additionally, multiple samples and calibrants are usually analyzed to assess accuracy of the measurement procedure and repeatability by the analyst. Thus, a realistic assessment of uncertainty for most chemical measurement methods is not purely bottom-up (based on the measurement equation) or top-down (based on the experimental design), but inherently contains elements of both. Confidence in results must be rigorously evaluated for the sources of variability in all of the bottom-up and top-down elements. This type of analysis presents unique challenges due to various statistical correlations among the outputs of measurement equations. One approach is to use a Bayesian hierarchical (BH) model which is intrinsically rigorous, thus making it a straightforward method for use with complex experimental designs, particularly when correlations among data are numerous and difficult to elucidate or explicitly quantify. In simpler cases, careful analysis using GUM Supplement 1 (MC) methods augmented with random effects meta analysis yields similar results to a full BH model analysis. In this article we describe both approaches to rigorous uncertainty evaluation using as examples measurements of 25-hydroxyvitamin D3 in solution reference materials via liquid chromatography with UV absorbance detection (LC-UV) and liquid chromatography mass spectrometric detection using isotope dilution (LC-IDMS).

中文翻译：

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化学测量不确定度的严格评估：使用检测器响应因子校准的液相色谱分析方法

化学测量方法旨在促进对被测量或系统的准确了解。因此，这些方法通常允许引出实验数据中可变性和相关性的潜在来源。他们通常实施支持量化与校准标准和其他已知或观察到的参数变量相关的影响的测量方程。此外，分析人员通常会分析多个样品和校准物，以评估测量程序的准确性和可重复性。因此，对大多数化学测量方法的不确定性的现实评估不是纯粹自下而上（基于测量方程）或自上而下（基于实验设计），而是固有地包含两者的元素。必须针对所有自下而上和自上而下要素的可变性来源对结果的信心进行严格评估。由于测量方程输出之间的各种统计相关性，这种类型的分析提出了独特的挑战。一种方法是使用本质上严格的贝叶斯分层 (BH) 模型，从而使其成为用于复杂实验设计的直接方法，特别是当数据之间的相关性众多且难以阐明或明确量化时。在更简单的情况下，使用 GUM Supplement 1 (MC) 方法和随机效应元分析进行仔细分析会产生与完整 BH 模型分析相似的结果。