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Download PDF by Emery N. Brown, Adam Sapirstein (auth.), Constantine: Case Studies in Bayesian Statistics, Volume II

By Emery N. Brown, Adam Sapirstein (auth.), Constantine Gatsonis, James S. Hodges, Robert E. Kass, Nozer D. Singpurwalla (eds.)

ISBN-10: 0387945660

ISBN-13: 9780387945668

ISBN-10: 1461225469

ISBN-13: 9781461225461

Like its predecessor, this moment quantity provides special functions of Bayesian statistical research, every one of which emphasizes the medical context of the issues it makes an attempt to unravel. The emphasis of this quantity is on biomedical purposes. those papers have been offered at a workshop at Carnegie-Mellon college in 1993.

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Jj=l Pj r "* (3) PJ+1 Steps 1-3 are repeated a large number of times B, giving estimates v;l, ... v;B. 3) in Brown and Sapirstein's paper, and using ). * IV;* in place of ). * in steps 2 and 3 above. Non-parametric bootstrap Instead of steps 1 and 2 above, for each segment j we sample CjI" .. cjL with replacement from Cjt, ... CjL. The estimates are then computed as in step 3 above. This procedure ignores the multinomial variability of the unobserved counts Xi> and uses the empirical distribution of the Cjl'S (rather than the Poisson model) to simulate the variability of the subsampling process.

A method for checking whether the variability is due to variance alone would be to inject at least two colors simultaneously into the rabbit. Any differences in the conclusions is due to variability, not to minute by minute differences in the rabbit. Statistical models for a multiple-rabbit version of BS's data would typically include additional measurement error beyond what the analysis of BS shows. The reason is that it would be hard to believe that BS's analysis could possibly find all sources of variability and oorrectly model them.

The analysis of BS does not account for the error in this number, but they apparently were already aware that the uncertainty does need to be accounted for. BS use log normals to model the uncertainty in several volumes. This apparently was motivated by a manufacturer's specification of a standard deviation as a fraction of the mean, which suggested a log normal to BS. However, many distributions have variances which increase as the mean squared, for example the N(p:, rp:2) density. Many of these alternative distributions may be more tractable than the log normal.

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Case Studies in Bayesian Statistics, Volume II by Emery N. Brown, Adam Sapirstein (auth.), Constantine Gatsonis, James S. Hodges, Robert E. Kass, Nozer D. Singpurwalla (eds.)


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