Bootstrap error-adjusted single-sample technique
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In statistics, the bootstrap error-adjusted single-sample technique (BEST or the BEAST) is a non-parametric method for estimating the distribution of a sample.[1] It is based on a statistical method called bootstrapping. BEST provides advantages over other methods such as the Mahalanobis metric, because it does not assume equal covariance for all spectral groups[clarification needed] or that each group is drawn for a normally distributed population.[2]A quantitative approach involves BEST along with nonparametric cluster analysis algorithm and multidimensional standard deviations (MDSs) between clusters and spectral data points can be calculated, where BEST considers each frequency to be taken from a separate dimension.[3] BEST is based off a population, P, relative to some hyperspace, R, that represents the universe of possible samples. P* is the realized values of P based on a calibration set, T. T is used to find all possible variation in P. P* is bound by parameters C and B. C is the expectation value of P, written E(P), and B is a bootstrapping distribution called the Monte Carlo approximation. Standard deviation can be found using this technique. The values of B projected into hyperspace give rise to X. The hyperline from C to X gives rise to the skew adjusted standard deviation which is calculated in both directions of the hyperline.[4]
Application
BEST is used in detection of sample tampering in pharmaceutical products. Valid (unaltered) samples are defined as those that fall inside the cluster of training-set points when the BEST is trained with unaltered product samples. False (tampered) samples are those that fall outside of the same cluster.[1]
Methods such as ICP-AES require capsules to be emptied for analysis. A nondestructive method is valuable. A method such as NIRA can be coupled to the BEST method in the following ways according to Hieftje et al.[1]
1) Detect any tampered product by determining that it is not similar to the previously analyzed unaltered product. 2) Quantitatively identify the contaminant from a library of known adulterants in that product. 3) Provide quantitative indication of the amount of contaminant present.
References
- ^ a b c Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1021/ac00142a008, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1021/ac00142a008instead. - ^ Attention: This template ({{cite jstor}}) is deprecated. To cite the publication identified by jstor:2685844, please use {{cite journal}} with
|jstor=2685844instead. - ^ Joseph Mendendorp and Robert A. Lodder (2006) "Acoustic-Resonance Spectrometry as a Process Analytical Technology for Rapid and Accurate Tablet Identification" AAPS PharmSciTech 7 (1) Article 25.
- ^ Sara J. Hamilton and Robert Lodder, "Hyperspectral Imaging Technology for Pharmaceutical Analysis", Society of Photo-Optical Instrumentation Engineers
Further reading
- Lodder, R.; Hieftje, G. (1988). "Quantile BEAST Attacks the False-Sample Problem in Near-Infrared Reflectance Analysis". Applied Spectroscopy. 42 (8): 1351–1365.
- Y. Zou, Robert A. Lodder (1993) "An Investigation of the Performance of the Extended Quantile BEAST in High Dimensional Hyperspace", paper #885 at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Atlanta, GA
- Y. Zou, Robert A. Lodder (1993) "The Effect of Different Data Distributions on the Performance of the Extended Quantile BEAST in Pattern Recognition", paper #593 at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Atlanta, GA
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