Bootstrap error-adjusted single-sample technique
 | This article may be too technical for most readers to understand. (March 2011) |
In statistics, the bootstrap error-adjusted single-sample technique (BEST or the BEAST) is a non-parametric method that is intended to allow an assessment to be made of the validity of a single sample. It is based on estimating a probability distribution representing what can be expected from valid samples.[1] This is done use a statistical method called bootstrapping, applied to previous samples that are known to be valid.
Methodology
[edit | edit source]BEST provides advantages over other methods such as the Mahalanobis metric, because it does not assume that for all spectral groups have equal covariances [clarification needed] or that each group is drawn for a normally distributed population.[2] A quantitative approach involves BEST along with a nonparametric cluster analysis algorithm. Multidimensional standard deviations[clarification needed] (MDSs) between clusters and spectral[clarification needed] data points are calculated, where BEST considers each frequency to be taken from a separate dimension.[clarification needed][3]
BEST is based on 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. The standard deviation can be found using this technique. The values of B projected into hyperspace give rise to X. The hyperline[definition needed] from C to X gives rise to the skew adjusted standard deviation which is calculated in both directions of the hyperline.[4]
Application
[edit | edit source]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[clarification needed] to be emptied for analysis. A nondestructive method is valuable. A method such as NIRA[clarification needed] can be coupled to the BEST method in the following ways.[1]
- Detect any tampered product by determining that it is not similar to the previously analyzed unaltered product.
- Quantitatively identify the contaminant from a library of known adulterants in that product.
- Provide quantitative indication of the amount of contaminant present.
References
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- ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- ^ 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 [full citation needed]
Further reading
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- 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