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Some thoughts about classification

The paper contains some general remarks on the high art of data analysis, some philosophical thoughts about classification, a partial review of outliers and robustness from the point of view of applications, including a discussion of the problem of model choice, and a review of several aspects of robust estimation of covariance matrices, including the pragmatic choice of a weight function based on empirical and theoretical evidence. Several sections contain new (or at least original) ideas: There are some proposals for incorporating robustness into Bayesian practice and theory, including weighted log likelihoods and Bayes’ theorem for weighted data. Some small ideas refer to artificial classification in a continuum, to a “robust” (Prohorov-type) metric for high-dimensional data, and to the use of multiple minimum spanning trees. A promising but difficult research idea for clustering on the real line, based on a new smoothing method, concludes the paper.