GY’s theory

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. 

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). 

An algorithm for the evaluation of the fundamental sampling error in the sampling of particulate solids, based on GY s theory, is described by MINKINNEN [1987]. 

Pierre Gy has written a number of papers and consolidated his work in several books. For simplicity, I quote mainly from his most recent books, one in 1992, consolidating his theory in its entirety, and his latest one in 1998, an abbreviated version that highlights the major elements. Francis Pitard has presented the essence of Gy s theory in a recent book and examined the idea of... 

The first steps in any sampling investigation are audit and assessment find out what is going on and whether the current sampling variation is acceptable. If not, then some way must be found to reduce it. This would be easier if the total variation could be broken down and the component parts addressed separately. Pierre Gy s theory does this. Gy (1992) decomposes the total variation into seven major components (sources). He calls them errors because sampling is an error-generating process, and these errors contribute to the nonrepresentativeness of the sample. The seven errors are as follows ... 

Therefore, sampling correctness has a special meaning in Gy s theory. When we talk about a correct sample, we mean that the principle of correct sampling has been followed. Note that correctness is a process, which we have some control over. We do not have control, however, over the accuracy of a sample value, which is a result. This is no different than SRS, where we can control the method by which we obtain a subset of the population of individual units using a random technique. But we are stuck with the resulting sample and its value of the characteristic of interest. 

Detailed discussions on the applications and other limitations of Gy s theory are provided by Ottley (1966), and on Ingamell s and Visemann s theories by Smith and James (1981). 

Gy s theory identifies, and proposes techniques for minimization of, seven major categories of sampling error, covering differences within samples. Other problems exist, including errors involving sampling over space (e.g., soil samples that provide a poor representation of a polluted site) and over time. The internal sample error categories are (Gy nomenclature) ... 

F.F. Pitard, Pierre Gy s sampling theory and sampling practice (2nd edn), CRC Press LLC, Boca Raton, 1993. 

Pitard, F.F. Pierre Gy s Sampling Theory and Sampling Practice, Vols. 1 and 2, CRC Press, Boca Raton/ Florida, 1989... 

Today, the entire statistics world is acquainted with Dr. Pierre Gy s gem called the sampling theory, which is the only sampling theory that is complete and founded on solid, scientific ground. After teaching several hundred courses around the world to many thousands of people on the virtues of the sampling theory, I came to the conclusion that three kinds of professionals attend these courses. 

See. for example. J. L. Devore and N. R. Farnum. Applied Statistics for Engineers and Scientists, pp. 158-166. Pacific Grove, CA Duxbury Press at Brooks/Cole Publishing Co.. 1999 J. C. Miller and J. N. Miller, Statistics and Chemometrics for Analytical Chemistry, 4th ed. Upper Saddle River, N.I Prentice-Hall, 2000 B. W. Woodget and D. Cooper, Samples and Standards. London Wiley, 1987 F.F. Pitard, Pierre Gy s Sampling Theory and Sampling Practice. Boca Raton, FL CRC Press, 1989. 

Sampling of Particulate Materials—Theory and Practice, Elsevier Scientific Publishing Co, New York, 1979, Pitard, Francis F, Pierre Gys Sampling Theory and Sampling Practice, CRC Press, Inc, Boca Raton, Florida, 1995, Gayle, G, B, Theoretical Precision of Screen Analysis, Report of Investigations No, 4993, U,S, Bureau of Mines, Dept, of Interior, Washington, D,C, 1952,... 

Gy s classical theory is a comprehensive theory for the sampling from heterogeneous materials developed on the basis of studying the sampling of granular materials. The simplest model expressed by eqn [31] can be modified according to Gy s sampling theory ... 

Gy s sampling theory can be expressed by a very simple equation ... 

The foregoing are very brief indications of the problems addressed by Gy s comprehensive theory (see also Figure 8.16) detailed discussions (Gy 2004) of these concepts provide complete explanations. An interesting discussion (Minkiimen 2004) describes use of these principles in optimization of real-world applications in the context of a fitness for purpose approach. The following... 

ENDOR = electron nuclear double resonance EPR = electron-paramagnetic resonance ESR = electron-spin resonance NMR = nuclear magnetic resonance MA = modulation amplitude SOFT = second-order perturbation theory s-o = spin-orbit zfs = zero-field splitting (for S > 1 /2) D = uniaxial zfs E = rhombic zfs g = g-factor with principal components gy, and g ge = free electron g-factor a = hyperfrne splitting constant A = hyperftne coupling constant for a given nucleus N (nuclear spin 7>0). 

Figure 13.10 Phase diagram for a conformationally symmetric diblock copolymer predicted by the mean-field theory, showing the regions where the equilibrium phases are disordered (DIS), lamellar (L), gy-roid (Gi33(])s hexagonal cylindrical (H), BCC cubic (i2im3m)> close-packed spheres (CPS, which is either face-centered cubic or hexagonally close-packed). (Reprinted with permission from Matsen and Bates, Macromolecules 29 1091. Copyright 1996, American Chemical Society.)...

Note also that the first equality in (8.10) can be defined for any Ra provided we use Ra as the upper limit of the integral in (8.6). The second and third equalities hold true only for Ra > Rc where Rc is the correlation distance in the system. Since we can obtain all the Gy from the inversion of the KB theory, we can also compute PS(i s) for each i and s. Clearly, for very large Ra, we have PS( i s) = 0. This makes sense, since for very large volume V , the local composition must approach the bulk composition, hence the PS of s with respect to all i will tend to zero. As with the local composition,... 

As we noted in Section 18.7, the variances of the mean plume dimensions can be expressed in terms of the motion of single particles released from the source. (At a particular instant the plume outline is defined by the statistics of the trajectories of two particles released simultaneously at the source. We have not considered the two-particle problem here.) In an effort to overcome the practical difficulties associated with using (18.72) to obtain results for Gy and gz, Pasquill (1971) suggested an alternate definition that retained the essential features of Taylor s statistical theory but that is more amenable to parametrization in terms of readily measured Eulerian quantities. As adopted by Draxler (1976), the American Meteorological Society (1977), and Irwin (1979), the Pasquill representation leads to... 

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