Prior, George

We thank Drs. Graham George and Roger Prince and the reviewers for useful comments and are grateful to Drs. Brian Hales and Graham George for Informing us of results prior to publications. 

These circumstances may explain why it took ten years for the phenomenon to be experimentally observed after the prediction. In 1973, prior to this finding, Lon Hocker, George Benedek, and Tanaka realized that a gel scattered light, and the light intensity fluctuated with time [5]. They established that the scattering is due to the thermal density fluctuations of the polymer network and derived a theory that explained the fluctuation. These fluctuations are similar to... 

George, A. and Veis, A. (1991) FTIRS in H2O demonstrates that collagen monomers undergo a conformational transition prior to thermal self-assembly in vitro. Biochemistry 30,2372-7. 

Horseradish peroxidase (and urease) played an important role in the development of the modern concept of the nature of an enzyme and the role of metal ions (Sumner and Somers, 1943 Willstatter, 1965). The species now known as compound II (HRP-II) formed as a result of the reaction of HRP with H202, was discovered in 1937 (Keilen and Mann, 1937). Later compound I (HRP-I), formed prior to HRP-II was identified (Theorell, 1941). The spectra of HRP-I and HRP-II in the 400 nm (Soret band) region have been determined (Chance, 1949 a, b) and measurements have also been extended to the visible region (Chance, 1952). Formation of HRP-I is first order in H202 and HRP (Chance, 1943) and the -OOH group is essential for the oxidation of HRP by peroxide. The enzymatic cycle can be summarised by the following equations (George, 1952),... 

A partially Bayesian approach was suggested by Chipman et al. (1997). They used independent prior distributions for each main effect being active. The prior distribution selected for Pj was a mixture of normals, namely, N(0, r ) with prior probability 1 — tzj and N(0, Cj if) with prior probability ttj, where Cj greatly exceeds 1. The prior distribution for a2 was a scaled inverse-x2. They then used the Gibbs-sampling-based stochastic search variable selection method of George and McCulloch (1993) to obtain approximate posterior probabilities for Pj, that is, for each factor they obtained the posterior probability that Pj is from /V(0, cj if) rather than from N(0, r ). They treated this as a posterior probability that the corresponding factor is active and used these probabilities to evaluate the posterior probability of each model. 

A variety of prior distributions has been proposed for the subset selection problem and most differ in terms of the distributions placed on /3 and 8. One particular formulation, due to Box and Meyer (1986) and George and McCulloch (1997), is reviewed in detail here. Subsequent examples use this particular formulation, although many issues that arise are general. 

George and McCulloch (1993) chose a prior distribution for /3 that does not... 

George and McCulloch (1997) also gave analytic results for a point mass mixture prior distribution (6). 

For the nonconjugate prior distribution (5), George and McCulloch (1993) and Chipman et al. (1997) used the Gibbs sampler to simulate the joint posterior distribution of (/3, a, 8) that is, the above algorithm had, within step 2, an extra substep to draw values of fli,..., fin from p((3 8, a, Y) and a substep to draw... 

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