statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, the bootstrap error-adjusted single-sample technique (BEST or the BEAST) is a

non-parametric Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparametric statistics is based on either being distri ...

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 In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon i ...

representing what can be expected from valid samples. This is done use a statistical method called

bootstrapping In general, bootstrapping usually refers to a self-starting process that is supposed to continue or grow without external input. Etymology Tall boots may have a tab, loop or handle at the top known as a bootstrap, allowing one to use fingers ...

, applied to previous samples that are known to be valid.

Methodology

BEST provides advantages over other methods such as the Mahalanobis metric, because it does not assume that for all spectral groups have equal

covariance In probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the les ...

s or that each group is drawn for a normally distributed population. A quantitative approach involves BEST along with a nonparametric

cluster analysis Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of ...

algorithm. Multidimensional standard deviations (MDSs) between clusters and spectral data points are calculated, where BEST considers each frequency to be taken from a separate dimension.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 Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is ...

approximation. The

standard deviation In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...

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.Sara J. Hamilton and Robert Lodder, "Hyperspectral Imaging Technology for Pharmaceutical Analysis", Society of Photo-Optical Instrumentation Engineers

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 Inductively coupled plasma atomic emission spectroscopy (ICP-AES), also referred to as inductively coupled plasma optical emission spectroscopy (ICP-OES), is an analytical technique used for the detection of chemical elements. It is a type of emiss ...

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. *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.

Methodology

Application

References

Further reading