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And Smith, J. Q. (1990). Influence Diagrams, Belief Nets and Decision Analysis. Wiley, London. 54. Wermuth, N. and Cox, D. R. (1997). On association models defined over independence graphs. Bernoulli, to appear. GRAPHICAL REPRESENTATION, COMPUTER AIDED 55. Wermuth, N. and Lauritzen, S. L. (1983). Graphical and recursive models for contingency tables. Biometrika, 70, 537–552. 56. Wermuth, N. and Lauritzen, S. L. (1990). On substantive research hypotheses, conditional independence graphs and graphical chain models (with discussion).

Figures 2, 3, and 4 show plots involving small amounts of data, which nevertheless require complicated calculations in order to draw them. Figure 2 displays the empirical cumulative distribution function∗ (ECDF) of 30 independent observations, superimposed on which is the theoretical cumulative distribution function (CDF) for the normal distribution, the mean and variance of which were estimated from the data (the usual x and s2 ). The normal CDF involves a complicated integral which cannot be evaluated explicitly.

In Statistics and Mathematics in Biology, O. , eds. Iowa State College Press, Ames, pp. 35–66. 51. Wermuth, N. (1976). Analogies between multiplicative models in contingency tables and covariances selection. Biometrics, 32, 95–108. 52. Wermuth, N. (1980). Linear recursive equations, covariance selection, and path analysis. J. Amer. Statist. , 75, 963–997. 38. Neapolitan, R. E. (1990). Probabilistic Reasoning in Expert Systems. Wiley, New York. 53. Wermuth, N. (1992). On block-recursive regression equations (with discussion).

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Encyclopedia of Statistical Scis. [Vol. 05] by S. Kotz


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