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New PDF release: Bayesian statistics, a review

By D V Lindley

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This has been discussed by Armitage (1963). Here, perhaps surprisingly, the sampling rule is noninformative and the likelihood is as usual, though, at least when n (now n) is large almost all the information is contained in it. Example 2. The following practical application is due to Roberts (1967). The situation is the capture-recapture analysis that is presumably familiar enough to omit a detailed description. The marriage between the natural notation in this context and that of this review is as follows: 9 -» N, the size of the population, of which R are tagged, x -> r, the number found to be tagged in a second sample of n, \l/ -> p, the chance of catching a fish (say) in that sample.

Incidentally the estimation of a2 presents some novel points which will be discussed at the end of § 8. *,• + e( with et = pei^1 + g,-. Again they conclude that the analysis is sensitive to the value of p (that is, a in the earlier notation). Larsen (1969) extends the discussion to the two-way, fixed effects, model. with and zero otherwise, so that there is correlation within rows but not otherwise. 33 These levels are approximately the posterior probabilities, given the data and a, that a\/a\ > 1.

Notice how the evaluation of L(t, x0) is effectively the evaluation of the sampling distribution of the sufficient statistic /(x). Consequently the results of the sampling-theory school are of value in preposterior analysis, though, as we have seen, in terminal analysis they are not needed because the likelihood principle obtains. The special case of the estimation of the mean of a normal distribution with known variance illustrates the ideas. 23). Equally, and with t — x0 + nx and N = n 0 + n.

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Bayesian statistics, a review by D V Lindley

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