By D. V. Lindley
A research of these statistical principles that use a chance distribution over parameter area. the 1st half describes the axiomatic foundation within the inspiration of coherence and the results of this for sampling concept records. the second one half discusses using Bayesian principles in lots of branches of records.
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Additional info for Bayesian Statistics. A Review
V. LINDLEY case of random sampling it is necessary to include the sample size as part of the (minimal) sufficient statistic. Notice that if 9 = (0i,0 2 ), marginal sufficiency for 6l is, in general, undefined. (For example, is s2 marginally sufficient for a2 in sampling from a normal distribution? ) If p(x|6) = p(t]\Bl)p(t2\G2] and the prior similarly factors, then ^(x) is marginally sufficient, but this is a very special case. The point arises in discussing robustness (§7). Exponential family.
In other words the finite population is equivalent to a random sample from a hyperpopulation. This assumption has been made by other writers but the justification in terms of exchangeability seems much stronger than any heretofore proposed. The same idea will occur in discussing other multiparameter problems below. 11) for /i and a2. „_ t is Student's t on n — 1 degrees of freedom and x and s2 are the usual sample mean and variance respectively. This is in close agreement with the usual theory.
This is in close agreement with the usual theory. The normality assumption is a severe, and often unreal, one. Ericson therefore also considers the case, mentioned above, where the 0's (and therefore the x's) take only a finite number T of possible values. 5)) and the relevant conjugate distribution is Dirichlet (this will be discussed in § 10 when considering Bayesian estimation of multinomial parameters). A typical result is that the posterior variance of n is approximately (N — n)/N • s2/n, in close agreement with orthodox theory.
Bayesian Statistics. A Review by D. V. Lindley