1,721,029 research outputs found
Application of mixture models to large datasets
No full textMixture distributions are commonly being applied for modelling and for discriminant and cluster analyses in a wide variety of situations. We first consider normal and t-mixture models. As they are highly parameterized, we review methods to enable them to be fitted to large datasets involving many observations and variables. Attention is then given to extensions of these mixture models to mixtures with skew normal and skew t-distributions for the segmentation of data into clusters of non-elliptical shape. The focus is then on the latter models in conjunction with the JCM (joint clustering and matching) procedure for an automated approach to the clustering of cells in a sample in flow cytometry where a large number of cells and their associated markers have been measured. For a class of multiple samples, we consider the use of JCM for matching the sample-specific clusters across the samples in the class and for improving the clustering of each individual sample. The supervised classification of a sample is also considered in the case where there are different classes of samples corresponding, for example, to different outcomes or treatment strategies for patients undergoing medical screening or treatment
An inequality for expectation of means of positive random variables
No full textSuppose that X, Y are positive random variables and m is a numerical (commutative) mean. We prove that the inequality E(m(X, Y )) leq m(E(X ), E(Y )) holds if and only if the mean is generated by a concave function. With due changes we also prove that the same inequality holds for all operator means in the Kubo–Ando setting. The case of the harmonic mean was proved by C. R. Rao and B. L. S. Prakasa Rao
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