Showing papers by "Herman Chernoff published in 1975"

Effect on Classification Error of Random Permutations of Features in Representing Multivariate Data by Faces

Abstract: A graphical method of representing multivariate data consists of drawing a cartoon of a face determined by 18 parameters. A sample of vector observations of dimension d ≤ 18 is converted to faces by assigning components of the vector to facial parameters. We report an experiment which estimates that the effect of a random permutation in the assignment of parameters may affect the error rate in a classification task using these faces by a factor of about 25 percent.

Personal probabilities of probabilities

Abstract: By definition, the subjective probability distribution of a random event is revealed by the (‘rational’) subject's choice between bets — a view expressed by F. Ramsey, B. De Finetti, L. J. Savage and traceable to E. Borel and, it can be argued, to T. Bayes. Since hypotheses are not observable events, no bet can be made, and paid off, on a hypothesis. The subjective probability distribution of hypotheses (or of a parameter, as in the current ‘Bayesian’ statistical literature) is therefore a figure of speech, an ‘as if’, justifiable in the limit. Given a long sequence of previous observations, the subjective posterior probabilities of events still to be observed are derived by using a mathematical expression that would approximate the subjective probability distribution of hypotheses, if these could be bet on. This position was taken by most, but not all, respondents to a ‘Round Robin’ initiated by J. Marschak after M. H. De-Groot's talk on Stopping Rules presented at the UCLA Interdisciplinary Colloquium on Mathematics in Behavioral Sciences. Other participants: K. Borch, H. Chernoif, R. Dorfman, W. Edwards, T. S. Ferguson, G. Graves, K. Miyasawa, P. Randolph, L. J. Savage, R. Schlaifer, R. L. Winkler. Attention is also drawn to K. Borch's article in this issue.