Theory of sampling

Two principal topics are considered under theory of sampling. First is theoiy accounting for physical properties of material to be sampled. Second is the process of mechanical sample extrac tion. The theoiy predicts accuracy of sample taking—how much sample to take and howto take it to meet an accuracy specification. 

Deming, W.E. (1950), Some Theory of Sampling, Wiley, New York, NY. 

Process Sampling Theory of Sampling the Missing Link in Process Analytical Technologies (PAT)... 

This new terminology is proposed jointly in the present publication and in Pitard Pierre Gy s Theory of Sampling and C.O. IngamelTs Poisson Process Approach — Pathways to Representative SampUng and Appropriate Industrial Standards . Doctoral thesis, Aalborg University, campus Esbjerg (2009). ISBN 978-87-7606-032-9. 

The fundamental principles for representative sampling and effective counteractions towards heterogeneity were delineated for batch sampling (0-D) as well as process sampling (1-D). All principles are contained in the theory of sampling (TOS). 

L. Petersen, P. Minkkinen and K. H. Esbensen, Representative sampling for reliable data analysis Theory of Sampling, Chemom. Intell. Lab. Syst., 77(1-2), 261-277 (2005). 

K.H. Esbensen and P. Minkkinen, Special Issue 50 years of Pierre Gy s Theory of Sampling. Proceedings First World Conference on Sampling and Blending (WCSBl). Tutorials on Sampling Theory and Practice, Chemom. Intell. Lab. Syst., 74(1), 236 (2004). 

AU multivariate calibrations must be based on empirical training and validation data sets obtained in fully realistic situations acoustic chemometrics is no exception. Many models are in addition based on indirect multivariate calibration. All industrial applications must always be evaluated only based on test set validation. Reference [2] deals extensively with the merits of the various validation methods, notably when it is admissible, and when not, to use cross-validation. See also Chapters 3 and 12, which give further background for the test set imperative in light of typical material heterogeneity and the Theory of Sampling . 

SERS surface enhanced Raman TOS theory of sampling... 

Petersen L, Minkkinen P, Esbensen KH. Representative sampling for reliable data analysis theory of sampling. Chemom Intell Lab Syst 2005 77 261-277. 

A common and exact theory of sampling of inhomogeneous materials with stochastic composition is presented by BRANDS [1983]. Because experimental evaluation of this theory involves some difficulties, it was verified by simulation experiments. 

Theory related to material characteristics states that a minimum quantity of sample is predicated as that amount required to achieve a specified limit of error in the sample-taking process. Theory of sampling in its application acknowledges sample preparation and testing as additional contributions to total error, but these error sources are placed outside consideration of sampling accuracy in theory of sample extraction. 

Variations in measurable properties existing in the bulk material being sampled are the underlying basis for sampling theory. For samples that correctly lead to valid analysis results (of chemical composition, ash, or moisture as examples), a fundamental theory of sampling is applied. The fundamental theory as developed by Gy (see references) employs descriptive terms reflecting material properties to calculate a minimum quantity to achieve specified sampling error. Estimates of minimum quantity assumes completely mixed material. Each quantity of equal mass withdrawn provides equivalent representation of the bulk. 

L vov B. V., Bayonov P. A. and Ryabchuk (1981) A macrokinetic theory of sample vaporization in electrothermal atomic absorption spectrometry, Spectrochim Acta, Part B 36 397-425. 

G. Brands, Theory of Sampling. I. Uniform Inhomogeneous Material, Fre-senius Z. Anal Chem., 314 (1983) 6 II. Sampling firom Segregated Material, Z. Anal Chem., 314 (1983) 646. 

The statistical theories of sampling are discussed by Allen (1990) who also describes, in considerable detail, a large number of sampling methods. BS 3406/1 (1986) also gives guidance on sampling, the sub-division of laboratory samples and the reporting of results. 

Visman developed the theory of sampling taking into consideration the effect of segregation. The experimentally estimated variance 1 is related to two sampling constants, a homogeneity constant A, which is similar to Ingamells constant, and a segregation constant B ... 

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