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This paper assesses algorithms proposed for constructing confidence ellipses in multidimensional scaling (MDS) solutions and proposes a new approach to interpreting these confidence ellipses via hierarchical cluster analysis (HCA). It is shown that the most effective algorithm for constructing confidence ellipses involves the generation of simulated distances based on the original multivariate dataset and then the creation of MDS maps that are scaled, reflected, rotated, translated, and finally superimposed. For this algorithm, the stability measure of the average areas tends to zero with increasing sample size n following the power model, An−B, with positive B values ranging from 0.7 to 2 and high R-squared fitting values around 0.99. This algorithm was applied to create confidence ellipses in the MDS plots of squared Euclidean and Mahalanobis distances for continuous and binary data. It was found that plotting confidence ellipses in MDS plots offers a better visualization of the distance map of the populations under study compared to plotting single points. However, the confidence ellipses cannot eliminate the subjective selection of clusters in the MDS plot based simply on the proximity of the MDS points. To overcome this subjective selection, we should quantify the formation of clusters of proximal samples. Thus, in addition to the algorithm assessment, we propose a new approach that estimates all possible cluster probabilities associated with the confidence ellipses by applying HCA using distance matrices derived from these ellipses. [ABSTRACT FROM AUTHOR]

This paper extends the Suzuki and Shimodora method [Suzuki R, Shimodora H. Pvclust: an R package for assessing the uncertainty in hierarchical clustering. Bioinformatics. 2006;22:1540–1542] for assessing uncertainty in hierarchical cluster analysis to multivariate datasets and examines the reliability of the simulated cluster probabilities in relation to the simulation method adopted. The extension is applied to squared Euclidean and Mahalanobis-type distances and employs three simulation methods, the Monte-Carlo and bootstrap methods, and a new proposed method, the distance distribution. The distance distribution method is very fast and gives satisfactory predictions for the distance, its standard deviation, skewness, and kurtosis. The performance of the Monte-Carlo method is equally satisfactory, whereas the bootstrap method usually gives acceptable predictions only for the distance. The distance distribution and Monte-Carlo methods give similar cluster probabilities. The bootstrap probabilities are not very different; thus this method can be used in datasets of unknown distance distribution. [ABSTRACT FROM AUTHOR]

Age-at-death estimation in a skeletal assemblage (target sample) is biased by the demographic profile of the material used for age prediction (training sample) when this profile is different from that of the target sample. This bias is minimized if the demographic profile of the target sample is properly taken into account in the method developed for age-at-death estimation. In the Bayesian approach this is accomplished via the informative prior. For methods based on regression, we propose two techniques: (a) using weighting factors taken from the demographic profile of the target sample, and (b) creating a new hypothetical training sample that has a demographic profile similar to that of the target sample. The two techniques, as well as the Bayesian approach, were tested using 532 artificial systems in which the age marker exhibited an eight-grade expression. It was found that depending on the criteria used for evaluation, the proposed approaches and especially the one based on a hypothetical training sample, may give better results than the Bayesian method in more than 90% of the systems studied. A basic prerequisite for the good performance of the proposed approaches is to select carefully the training sample. This sample should exhibit a uniform demographic profile or a profile with almost equal numbers of young and older individuals. All the above hold if the training and the target samples have different demographic profiles. If the profiles are the same or very similar, the best aging method is the direct regression using simple linear models. [ABSTRACT FROM AUTHOR]

The combined effect of temperature, T, and organic modifier concentration, phi, on the retention under gradient conditions in RPLC is studied by considering, both theoretically and experimentally gradients, of phi at constant T and gradients of T at constant phi. Two approaches are examined: in the first approach the prediction of the elution time of a sample solute is based on the isocratic/isothermal properties of this solute. The second approach is based on a direct fitting procedure of a proper retention model to 2-D isocratic/T-gradient or isothermal/phi-gradient retention data. These approaches were tested using alkylbenzes in eluting systems modified by ACN. We found that both approaches can give excellent predictions under certain prerequisites. However, the first approach exhibits the notable advantage that it can be used effectively to predict retention times under any kind of phi-gradients at constant T or T-gradients at constant phi. The second approach has the advantage that it is relatively simple but its applicability is very restricted since its predictions are satisfactory only if the gradients are of the same kind with those used in the fitting procedure and the conditions lie within those used for fitting.