Decision-theoretical formulation of thecalibration problem

[摘要] The choice of calibration policy is of basic importance in analyticalchemistry. A prototype of the practical calibration problem isformulated as a mathematical task and a Bayesian solution of theresulting decision problem is presented. The optimum feedbackcalibration policy can then be found by dynamic programming. Theunderlying parameter estimation and filtering are solved byupdating relevant conditional distributions. In this way: thenecessary information is specified (for instance, the need forknowledge of the probability distribution of unknown samples isclearly recognized as the conceptually unavoidable informationalsource); the relationship of the information gained from acalibration experiment to the ultimate goal of calibration, i.e., tothe estimation of unknown samples, is explained; an ideal solutionis given which can serve for comparing various ways of calibration;and a consistent and conceptually simple guideline is given forusing decision theory when solving problems of analytical chemistrycontaining uncertain data. The abstract formulation is systematicallyillustrated by an example taken from gas chromatography.

[学科分类] 分析化学