A Bayesian Approach to Nonlinear Calibration Problems
非线性校准问题的贝叶斯方法AI 解读 ↓
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非线性校准问题的贝叶斯方法
- 研究问题
- 当生物测定的浓度与反应关系明显非线性，且样本不能稀释时，如何进行低浓度校准并降低大量样本计算的负担？
- 方法与思路
- 作者提出贝叶斯非线性校准的近似计算方法，以验证子样本和高斯求积作精度比较，并展示两种生物测定结果的组合。
- 材料陈述的贡献
- 摘要称，该近似方法旨在减少常规贝叶斯积分的计算量，并以农业土壤样本中的化学物浓度测定展示校准与测定组合。
- 阅读关注点
- 应核对反应曲线与先验设定、近似计算的具体步骤、验证样本的选取，以及两种测定结果组合时如何处理不确定性。
- 阅读边界
- 仅据稿件版本未注明的 OpenAlex 索引摘要；未报告近似误差、计算节省幅度或适用曲线范围，不能认定其在所有低浓度情形下准确。
原文摘要
In bioassays, enzyme assays, or radioimmunoassays the concentration response relationships are mostly nonlinear. Very often because of physical restrictions or for biological reasons, the prediction samples cannot be diluted and the determination of very low concentrations is of interest. Thus one cannot be restricted to the “almost linear” part of the response curve and standard linear calibration methods are not applicable. The nonlinear calibration problem is of great importance in these types of applications. To implement the Bayesian paradigm in nonlinear calibration problems, a substantial amount of numerical integration is necessary. In practice, when concentrations of hundreds of samples have to be determined routinely, even with a highly efficient integration method (Naylor and Smith 1982), the numerical effort becomes prohibitive. An approximation method is proposed, therefore, to reduce the calculation. The precision of the approximation method is examined by validation subsamples and comparison with an integration routine based on the Gaussian quadrature strategy. An example from agricultural research is used to illustrate the underlying problem. To determine the concentrations of an agrochemical present in soil samples taken at different time points from the field, two different bioassays were performed. The plant used in one assay is extremely sensitive at low concentrations, whereas the plant used in the other assay reacts at higher concentrations. Combination of results from the two assays is also demonstrated.