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Summary This paper deals with the Bayesian analysis of the additive mixed model experiments. Consider b randomly chosen subjects who respond once to each of t treatments. The subjects are treated as random effects and the treatment effects are fixed. Suppose that some prior information is available, thus motivating a Bayesian analysis. The Bayesian computation, however, can be difficult in this situation, especially when a large number of treatments is involved. Three computational methods are suggested to perform the analysis. The exact posterior density of any parameter of interest can be simulated based on random realizations taken from a restricted multivariate t distribution. The density can also be simulated using Markov chain Monte Carlo methods. The simulated density is accurate when a large number of random realizations is taken. However, it may take substantial amount of computer time when many treatments are involved. An alternative Laplacian approximation is discussed. The Laplacian method produces smooth and very accurate approximates to posterior densities, and takes only seconds of computer time. An example of a pipeline cracks experiment is used to illustrate the Bayesian approaches and the computational methods.

Consider the logistic linear model, with some explanatory variables overlooked. Those explanatory variables may be quantitative or qualitative. In either case, the resulting true response variable is not a binomial or a beta-binomial but a sum of binomials. Hence, standard computer packages for logistic regression can be inappropriate even if an overdispersion factor is incorporated. Therefore, a discrete exponential family assumption is considered to broaden the class of sampling models. Likelihood and Bayesian analyses are discussed. Bayesian computation techniques such as Laplacian approximations and Markov chain simulations are used to compute posterior densities and moments. Approximate conditional distributions are derived and are shown to be accurate. The Markov chain simulations are performed effectively to calculate posterior moments by using the approximate conditional distributions. The methodology is applied to Keeler's hardness of winter wheat data for checking binomial assumptions and to Mat...

SUMMARY A simple procedure is proposed for exact computation to smooth Bayesian estimates for logistic regression functions, when these are not constrained to lie on a fitted regression surface. Exact finite sample inferences and predictions are available, together with an exact residual analysis. The prior distribution relates to O'Hagan's assumptions for a normal regression function. A global shrinkage parameter and local smoothness parameter can be evaluated from the current data by hierarchical Bayesian procedures. Consideration of the shrinkage parameter permits an overall check regarding a hypothesised regression model. No optimisation technique is needed, since Monte Carlo simulations from independent logistic distributions can be directly employed. The complexity of the computations does not substantively increase with the dimensionality of the design space.

An exact Bayesian analysis can be performed for normal theory variance components models, using importance sampling. But remarkably accurate approximations are available using the Laplacian T-approximation introduced by Leonard, Hsu, and Ritter. Instead of maximizing the joint posterior density, conditional upon the parameter of interest, a device described by O'Hagan is used first. The Bayesian estimators are compared to the Lindley—Stein shrinkage estimators and the Lindley—Smith joint modal estimators. It is confirmed that joint modes can overcollapse toward prior hypotheses, when compared with more sensible Bayesian procedures. This is referred to as a “collapsing phenomenon.” A numerical example from the one-way random-effects model is considered, and the risks of the different estimators are simulated under a variety of loss functions. It is concluded that although the Lindley—Stein estimator performs well, a full hierarchical Bayesian analysis performs at least equally well, while permitti...

The optical and electrical properties of Ni(5 nm)-Au(5 nm) and Ni(3.5 nm)-indium tin oxide (ITO) (60 nm) films were studied. It was found that the normalized transmittance of Ni/ITO film could reach 87% at 470 nm, which was much larger than that of the Ni-Au film. It was also found that the specific contact resistance was 5 /spl times/ 10/sup -4/ /spl Omega/ /spl middot/ cm/sup 2/ and 1 /spl times/ 10/sup -3/ /spl Omega/ /spl middot/ cm/sup 2/, respectively, for Ni-Au and Ni/ITO on p-GaN. Furthermore, it was found that the 20 mA output power of light-emitting diode (LED) with Ni-Au p-contact layer was 5.26 mW. In contrast, the output power could reach 6.59 mW for the LED with Ni/ITO p-contact layer.

Three series of Au(I)-imidazole complexes with stoichiometries of [Au(Cn-bim)Cl], [Au(Cn-im)Cl], and [Au(Cn-im)2][NO3] x 2H2O (Cn-bim = N-CnH2n+1 -substituted benzimidazole and Cn-im = N-CnH2n+1-substituted imidazole) together with the compound of [Au(C18-bim)2][NO3] are synthesiszed. Typical structures of each series are determined by single crystal X-ray diffraction. The last series of compounds, are liquid crystals, and exhibit a wider mesophase range than their Ag(I) analogues. These Au(I) complexes form Au nanostructures both through chemical reduction or thermolysis. For the first time, N-long chain imidazole is utilized to stabilize colloidal Au in solution. Also for the first time, unique examples of simple thermolysis to produce large Au plates of nanothickness are demonstrated. Formation of a plate-like morphology through fusion of sphere-like nanoparticles at an early stage is evidenced by TEM images.

A method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters, thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite. Possibly tedious numerical integrations are replaced by conditional maximizations, which are shown to be quite accurate in a number of special cases. There are similarities with the profile likelihood ideas originated by Kalbfleisch and Sprott (1970), and the method is contrasted with a Laplacian approximation recommended by Kass, Tierney, and Kadane (1988, in press), referred to here as the “KTK procedure.” The methods are used to approximate the marginal posterior densities of the log-linear interaction effects and an overall measure of association in a two-way contingency table. Snee's (1974) hair/eye color data are reanalyzed, and adjustments are proposed to Goodman's (1964) analysis for the full-rank interaction model. Another application concerns marginaliz...