# Bootstrap error-adjusted single-sample technique
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{{technical|date=March 2011}}
In [statistics](/source/statistics), the '''bootstrap error-adjusted single-sample technique''' ('''BEST''' or '''the BEAST''') is a [non-parametric](/source/Non-parametric_statistics) 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](/source/probability_distribution) representing what can be expected from valid samples.[{{Cite journal | last1 = Lodder | first1 = Robert A. | last2 = Selby | first2 = Mark. | last3 = Hieftje | first3 = Gary M. | title = Detection of capsule tampering by near-infrared reflectance analysis | doi = 10.1021/ac00142a008 | journal = [Analytical Chemistry](/source/Analytical_Chemistry_(journal)) | volume = 59 | issue = 15 | pages = 1921–1930| year = 1987 }}] This is done use a statistical method called [bootstrapping](/source/Bootstrapping_(statistics)), applied to previous samples that are known to be valid.
==Methodology==
BEST provides advantages over other methods such as the [Mahalanobis metric](/source/Mahalanobis_distance), because it does not assume that for all spectral groups have equal [covariance](/source/covariance)s {{Clarify|date=February 2011}} or that each group is drawn for a [normally distributed population](/source/Normal_distribution).[{{Cite journal | last1 = Efron | first1 = B. | last2 = Gong | first2 = G. | title = A Leisurely Look at the Bootstrap, the Jackknife, and Cross-Validation | journal = [The American Statistician](/source/The_American_Statistician)| volume = 37 | issue = 1 | pages = 36–48 | doi = 10.2307/2685844 | year = 1983 | jstor = 2685844 }}] A quantitative approach involves BEST along with a nonparametric [cluster analysis](/source/cluster_analysis) algorithm. Multidimensional standard deviations{{Clarify|date=March 2011}} (MDSs) between clusters and spectral{{Clarify|date=March 2011}} data points are calculated, where BEST considers each frequency to be taken from a separate dimension.{{Clarify|date=March 2011}}[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.]
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](/source/Monte_Carlo_method) approximation. The [standard deviation](/source/standard_deviation) can be found using this technique. The values of B projected into hyperspace give rise to X. The hyperline{{definition needed|date=February 2022}} from C to X gives rise to the skew adjusted standard deviation which is calculated in both directions of the hyperline.[Sara J. Hamilton and Robert Lodder, "Hyperspectral Imaging Technology for Pharmaceutical Analysis", Society of Photo-Optical Instrumentation Engineers {{full citation needed|date=November 2012}}]
==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.[
Methods such as [ICP-AES](/source/ICP-AES) require capsules{{clarify|reeason=what are capsules to do with what is going on|date=March 2011}} to be emptied for analysis. A [nondestructive](/source/Nondestructive_testing) method is valuable. A method such as NIRA{{Clarify|date=March 2011}} can be coupled to the BEST method in the following ways.][
*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 ==
{{Reflist}}
==Further reading==
*{{cite journal| first1=R.|last1= Lodder |first2= G.|last2= Hieftje |title=Quantile BEAST Attacks the False-Sample Problem in Near-Infrared Reflectance Analysis| journal= Applied Spectroscopy |volume=42| pages=1351–1365| year=1988 |url=http://www.opticsinfobase.org/abstract.cfm?URI=as-42-8-1351| issue=8 | doi=10.1366/0003702884429652|bibcode= 1988ApSpe..42.1351L |s2cid= 67835182 |url-access=subscription}}
*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
Category:Resampling (statistics)
Category:Computational statistics
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