By D. V. Lindley

A examine of these statistical rules that use a chance distribution over parameter house. the 1st half describes the axiomatic foundation within the idea of coherence and the results of this for sampling concept statistics. the second one half discusses using Bayesian principles in lots of branches of records.

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**Sample text**

3 e (0"2 Known) Suppose y' = (YI' .. , Yn) is a random sample from a Normal distribution N(e, 0"2), where 0" is a supposed known. 2. 14) , the likelihood function of is e I(e I 0", y) oc. 1) where, as before, y is the average of the observations. The standardized likelihood function of is graphically represented by a Norma l curve located by y, with standard deviation O"/y'n. 1 (a) shows a set of standardized likelihood curves which could result from an experiment in which n = 10 and 0" = l. Three different situations are illustrated with data giving averages of y = 6, Y = 9, and y = 12.

L) - -I -;;2 2 ( . n oJ.. I =-::0-. 42) J.. J. 43) 1/2, and

3 25 densi ty. Thus, for independent observations Y(, .. "~ n' the posterior distribution can be written n 11 pee I Y(, .. , Yn) oc p(O) P(Yi 18) . 20) ;=1 and, for sufficiently large 11, the 11 terms introduced by the likelihood will tend to overwhelm the single term contributed by the prior [see Savage, (1954)]. An illuminating iJlustration of the robustness of inference, under sensible modification of the prior, is provided by the study of Mosteller and Wallace (1964) on disputed authorship.