# Bayesian Inference in Statistical Analysis (Wiley Classics by George E. P. Box, George C. Tiao By George E. P. Box, George C. Tiao

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Additional resources for Bayesian Inference in Statistical Analysis (Wiley Classics Library)

Example text

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. Now it could happen that the quantity of immediate scientific I interest was not itself but the reciprocal K = .

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. The above arguments indicate only that arbitrariness in the choice of the transformation in terms of which the prior is supposed locally uniform is often not catastrophic and that effects on the posterior distribution are likely to be of order 11- 1 and not of order I in relation to the data .

We consider flfst the case of a single parameter. 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.