Evaluation of analytical methods using signal-noise ratio as a statistical criterion

SN ratio is undoubtedly an interesting criterion and is especially useful in the case of physical tests in which values obtained are a kind of definition. It has little advantage for the evaluation or selection of the usual chemical analysis methods, because SN ratio varies in proportion to the differences of precision of each method.     

Human errors and reliability of test results in analytical chemistry

The present paper is a review of the main theoretical and technical aspects of human error treatment (error modelling, reduction and quantification) as applied in aviation, engineering, medicine and other fields. The aim of the review is to attract the attention of analysts and specialists in metrology and quality in chemistry to the human error problem and its influence on the reliability of test results of chemical composition and associated measurement uncertainty. Therefore, the subject of human error is interpreted in the review in application to the conditions of a chemical analytical laboratory.     

Decomposition of multicomponent mass spectra using Bayesian probability theory

We present a method for the decomposition of the mass spectra of mixed gases using Bayesian probability theory. The method works without any calibration measurement and therefore applies also to the analysis of spectra containing unstable species. For the example of mixtures of three different hydrocarbon gases the algorithm provides concentrations and cracking coefficients of each mixture component and also their confidence intervals. The amount of information needed to obtain reliable results and its relation to the accuracy of our analysis are discussed.     

Criterion for quantifying the reliability of analytical results in method development and evaluation

An important characteristic in judging analytical results for their suitability for a particular use is the reliability of the results. A procedure is developed for quantifying the reliability in a single measure, the maximum total error. This measure comprises both the bias and the precision of the results, and takes account of the statistical uncertainty of these estimates. The applicability of the procedure in method development and method evaluation is illustrated by means of a practical example, the flow-injection determination of orthophosphate.     

First analytical results using a multi-ion counting system of a spark source mass spectrometer

Isotope dilution measurements of geological reference materials are described using a newly developed multi-ion counting (MIC) system for a spark source mass spectrometer. Compared with the conventional photoplate detection system, there are considerably improved analytical features of the MIC system, especially the high sensitivity which leads to short measuring times of 1 min to 1 h for trace element analysis on the μg/g — ng/g level.     

Evaluating uncertainty in analytical measurements: the pursuit of correctness

 Simple in principle, the evaluation of uncertainty, especially in chemical analysis, is not a routine task and needs great care to be correct. This can be seen, particularly, from an examination of the EURACHEM Guide, Quantifying Uncertainty in Analytical Measurement (1995), which is the most important document on the subject. The examination reveals, in the author's opinion, a shortage of correctness in some principal details of the uncertainty estimation process as presented in worked examples in the Guide, and the author has therefore formulated some "in pursuit of correctness" rules for estimating uncertainty. The rules and respective comments are concerned with the following items: (1) choosing an appropriate distribution function in type B evaluation of uncertainty, (2) the necessity for consideration of separate contributions to the combined uncertainty, and (3) taking account of actual influence factors in the uncertainty estimation process. Furthermore, the problem of estimation of conditional versus overall uncertainty is touched upon in connection with comparative trials where only internal consistency of results is required. Received: 29 January 1998 · Accepted: 10 February 1998     

Skew‐normal linear calibration: a Bayesian perspective

In this paper, we present a Bayesian approach for estimation in the skew‐normal calibration model, as well as the conditional posterior distributions which are useful for implementing the Gibbs sampler. Data transformation is thus avoided by using the methodology proposed. Model fitting is implemented by proposing the asymmetric deviance information criterion, ADIC, a modification of the ordinary DIC. We also report an application of the model studied by using a real data set, related to the relationship between the resistance and the elasticity of a sample of concrete beams. Copyright © 2008 John Wiley & Sons, Ltd.     

Verification of results to improve the quality of analytical data: a proposal

After some two decades insisting on validation and normalization of methods, the reliability of the results in analytical chemistry continues to be unsatisfactory. Further, the processes involved are too slow, with the effect that frequently the most relevant results are obtained with methods not (yet) validated according to norms. It is time to rethink about how the reliability of the results could be improved. It is proposed to shift some of the control from the validation and normalization of method to the verification of the results, using verification tools built into the procedure: additional standards may enable the calculation of the yield of an extraction or chemical transformation, control the column performance or ensure that the fraction from a preseparation is correctly cut. Such verification tools provide control for every sample. If the correctness of results is verified for every sample, this confirms the adequate performance of the method and could replace a corresponding part of the validation. Examples are shown for a number of methods.     

Fluid-fluid correlation through a model charged membrane: analytical results

We study the properties of electrical double layers separated by a charged plate of finite thickness. The nonlinear Poisson-Boltzmann equation is analytically solved for this system. It is shown that, for an unsymmetrically charged, narrow plate, the charged fluids at both sides of the plate are strongly correlated, and the local electroneutrality condition (LEC) is not satisfied. The LEC is satisfied only for an infinitely thick plate. Analytical expressions for the induced charge and mean electrostatic potential are given and analyzed. These findings could be relevant for the understanding of protein adsorption on membranes.     

Estimating complicated baselines in analytical signals using the iterative training of Bayesian regularized artificial neural networks

The present work deals with the development of a new baseline correction method based on the comparative learning capabilities of artificial neural networks. The developed method uses the Bayes probability theorem for prevention of the occurrence of the over-fitting and finding a generalized baseline. The developed method has been applied on simulated and real metabolomic gas-chromatography (GC) and Raman data sets. The results revealed that the proposed method can be used to handle different types of baselines with cave, convex, curvelinear, triangular and sinusoidal patterns. For further evaluation of the performances of this method, it has been compared with benchmarking baseline correction methods such as corner-cutting (CC), morphological weighted penalized least squares (MPLS), adaptive iteratively-reweighted penalized least squares (airPLS) and iterative polynomial fitting (iPF). In order to compare the methods, the projected difference resolution (PDR) criterion has been calculated for the data before and after the baseline correction procedure. The calculated values of PDR after the baseline correction using iBRANN, airPLS, MPLS, iPF and CC algorithms for the GC metabolomic data were 4.18, 3.64, 3.88, 1.88 and 3.08, respectively. The obtained results in this work demonstrated that the developed iterative Bayesian regularized neural network (iBRANN) method in this work thoroughly detects the baselines and is superior over the CC, MPLS, airPLS and iPF techniques. A graphical user interface has been developed for the suggested algorithm and can be used for easy implementation of the iBRANN algorithm for the correction of different chromatography, NMR and Raman data sets.     

The structural properties of a two-Yukawa fluid: Simulation and analytical results

Standard Monte Carlo simulations are carried out to assess the accuracy of theoretical predictions for the structural properties of a model fluid interacting through a hard-core two-Yukawa potential composed of a short-range attractive well next to a hard repulsive core, followed by a smooth, long-range repulsive tail. Theoretical calculations are performed in the framework provided by the Ornstein-Zernike equation, solved either analytically with the mean spherical approximation (MSA) or iteratively with the hypernetted-chain (HNC) closure. Our analysis shows that both theories are generally accurate in a thermodynamic region corresponding to a dense vapor phase around the critical point. For a suitable choice of potential parameters, namely, when the attractive well is deep and/or large enough, the static structure factor displays a secondary low-Q peak. In this case HNC predictions closely follow the simulation results, whereas MSA results progressively worsen the more pronounced this low-Q peak is. We discuss the appearance of such a peak, also experimentally observed in colloidal suspensions and protein solutions, in terms of the formation of equilibrium clusters in the homogeneous fluid.     

Global comparability of analytical results

 Global decisions made on the basis of chemical analytical results need global comparability. The concept of traceability is important and necessary but not sufficient to achieve global comparability, especially for routine analysis in environmental protection, health care and public safety. Sometimes comparability is only determined by the method. In this case validated methods have to be known and recognized internationally. In addition, a minimum level of proficiency of the personnel producing analytical results has to be guaranteed. Finally, a system of measures designed to build up trust is needed for worldwide acceptance of analytical results. The method of self-declaration by the supplier of chemical analytical services has the advantage of presenting specific responsibility and gaining a good reputation. Additional methods should be employed. The evaluation of reference materials by specific quality criteria is mentioned as an example. Received: 1 July 1998 · Accepted: 20 July 1998     

Assuring trueness of analytical results

Summary A true analytical result presumes an analytical procedure without systematic errors. They can be detected by comparing the analytical results with the true value or with an accepted reference. Systematic errors are always superimposed by the random error, therefore such a comparison must include statistical tests. The paper describes suitable test-models for typical analytical problems, as e.g. the validation of an analytical procedure or the (current) control of analytical work. Furthermore, explanations will be given for the interpretation of the test results due to the trueness of analytical data and for the consequences concerning analytical work.     

Interpretation of the measurement results near the detection limit in gamma-ray spectrometry using Bayesian statistics

The requirement that the true value of an activity cannot be negative is used for the transformation of raw observed values, which can be positive or negative, into the expected activity values. The probability distribution of the activity values is a truncated Gaussian distribution, and the expected value and the variance of the activity values are derived from the observed value and its standard deviation. It has been shown that the standard deviation of the activity values is smaller than the standard deviation of the observed value and that the ratio of the standard deviation of the activity values and the expected value is less than unity. Since the expected activity value is larger than the original observed value, and the standard deviation of the activity values is smaller than the standard deviation of the observed value, the additional information, that the activity cannot be negative, leads to an improvement in the result. However, since the expected activity value depends on the standard deviation of the observed value, conservatively assessed standard deviation lead to a bias of the expected activity values.     

Computer simulation of the uncertainty of analytical results

Uncertainty is an important quality parameter of any analytical result. Estimating the uncertainty of analytical procedures can be rather difficult in many instances. Computer simulation based on multiple repetition of calculation of the resulting quantity while varying slightly the input parameters is an alternative option. The input parameters for the various computation runs are composed of two terms: the constant mean value and the error, obtained as the product of the standard uncertainty of the parameter in question and a random number with the normal distribution N(0.1). This approach can also serve to optimize measuring procedures, as demonstrated on an example of the determination of lead in biological materials by isotope dilution mass spectrometry. The accuracy of the optimized method was tested by analysis of some CRMs, the robustness of the method was examined, and the detection limit (10 ng/g Pb) and repeatability (4 ng/g Pb) were determined. Received: 30 September 1998 / Revised: 3 December 1998 / Accepted: 8 December 1998     

Computer simulation of the uncertainty of analytical results

Uncertainty is an important quality parameter of any analytical result. Estimating the uncertainty of analytical procedures can be rather difficult in many instances. Computer simulation based on multiple repetition of calculation of the resulting quantity while varying slightly the input parameters is an alternative option. The input parameters for the various computation runs are composed of two terms: the constant mean value and the error, obtained as the product of the standard uncertainty of the parameter in question and a random number with the normal distribution N(0.1). This approach can also serve to optimize measuring procedures, as demonstrated on an example of the determination of lead in biological materials by isotope dilution mass spectrometry. The accuracy of the optimized method was tested by analysis of some CRMs, the robustness of the method was examined, and the detection limit (10 ng/g Pb) and repeatability (4 ng/g Pb) were determined. Received: 30 September 1998 / Revised: 3 December 1998 / Accepted: 8 December 1998     

How good is good agreement: Evaluating the reliability of quantum-mechanically calculated observables

The practical value of a wave function derives from its ability to estimate or predict the chemical and physical properties of the electronic structure which it describes. Reliability is defined as a property to be evaluated on the basis of (i) the magnitude of the difference between the measured and calculated values of the observable together with (ii) the sign of the difference, (ii) the number and nature of observables correctly estimated, and (iv) the number and type of electronic structures that are correctly estimated. Systematic statistical comparison implies the existence of both internally consistent sets of wave functions for homologous series of molecules and their corresponding experimental values together with reliable error estimates. The most complete data base currently available for comparison is the spectroscopic constants for the first and second row diatomic hydrides. Utilizing appropriate statistical comparison techniques, four approximations (CEPA , PNO -CI , GTO -SCF , and STO -SCF ) are compared among themselves and against experimentally measured values. The CEPA approximation yields differences from experiment that approximate a normal error distribution, while the other approximations show systematic departures from experiment. Two values, ω_e and ω_eχ_e, for SH exhibit differences large enough to cast doubt upon the calculated value, the experimental value, or both.     

Analysis of multicomponent mass spectra applying Bayesian probability theory

In this paper we develop a method for the decomposition of mass spectra of gas mixtures, together with the relevant calibration measurements. The method is based on Bayesian probability theory. Given a set of spectra, the algorithm returns the relative concentrations and the associated margin of confidence for each component of the mixture. In addition to the concentrations, such a data set enables the derivation of improved values of the cracking coefficients of all contributing species, even for those components for which the set does not contain a calibration measurement. This latter feature also allows one to analyze mixtures that contain radicals in addition to stable molecules. As an example, we analyze and discuss the mass spectra obtained from the pyrolysis of azomethane, which contain the radical CH3 apart from nitrogen and C1- and C2-hydrocarbons.     

Conditional probability: a new fusion method for merging disparate virtual screening results

This paper introduces a new consensus scoring approach for merging the results of different virtual screening methods based on conditional probabilities. The technique is experimentally evaluated using several ligand-based virtual screening methods and compared to two variations of the established Sum-rank fusion method where it performs as well or better than the Sum-rank methods. Our experiments confirm that consensus scoring increases the number of active compounds retrieved with respect to the best individual methods on average.