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For, when O'~ -> co, in the limit the prior density becomes uniform over the entire line from - co to 00, and is therefore not a proper density function, Furthermore, it represents a situation where all values of 0 from - co to 00 are equally acceptable a priori. But it is difficult, if not impossible, to imagine a practical situation where sufficiently extreme values could not be virtually ruled out. 2 Nature of Bayesian Inference 21 where 11'0 is small compared with 11'", that is, where the prior is locally flat so that the likelihood dominates the prior.

In general , a prior wh ich is domInated by the likelihood is one which does not change very much o ver the region in which the likelihood is appreciable and does not assume large values out side that range (see Fig. 2) . We shall refer to a prior distributi o n which has these properties as a loca//y lIm/orm prior. 2 . I 6) for the very special case of a 1\iormal prior dominated by a Normal likelihood . Difficulties Associated \\ilh Loea//;: L'niform Priors Historically, the choice of a prior to characterize a situation where "nothing (or, more realistically, little) is known a priori" has long been, and still is, a matter of dispute.

3 This says that when we sample till the number of successes reaches a certain value some downward adjustment of probability is needed relative to sampling with Axed 11. We find this result much less surprising than the claim that they ought to agree. Tn general we feel that it is sensible to choose a noninformative prior which expresses ignorance re/alive to information which can be suppJied by a particular experiment. If the experiment is changed, then the expression of relative ignorance can be expected to change correspondingly.