Finite element analysis of a composite material interface

A finite element model of a composite material interface is developed to study the influence of the interface on the thermal strain in the composite. A plane stress model is used with an axisymmetric model as a check. The interface thickness, thermal coefficient, modulus, Poisson's ratio and the percent of mineral in the composite are variables in the study. The results confirmed the usability of the finite element model in studying the polymer-mineral interface

Consistency of Bayesian Linear Model Selection With a Growing Number of Parameters

Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which provide a stochastic search of informative variables, have gained popularity. In this paper, we will study the asymptotic properties related to Bayesian model selection when the model dimension $p$ is growing with the sample size $n$. We consider $p\le n$ and provide sufficient conditions under which: (1) with large probability, the posterior probability of the true model (from which samples are drawn) uniformly dominates the posterior probability of any incorrect models; and (2) with large probability, the posterior probability of the true model converges to one. Both (1) and (2) guarantee that the true model will be selected under a Bayesian framework. We also demonstrate several situations when (1) holds but (2) fails, which illustrates the difference between these two properties. Simulated examples are provided to illustrate the main results

Analysis of binary spatial data by quasi-likelihood estimating equations

The goal of this paper is to describe the application of quasi-likelihood estimating equations for spatially correlated binary data. In this paper, a logistic function is used to model the marginal probability of binary responses in terms of parameters of interest. With mild assumptions on the correlations, the Leonov-Shiryaev formula combined with a comparison of characteristic functions can be used to establish asymptotic normality for linear combinations of the binary responses. The consistency and asymptotic normality for quasi-likelihood estimates can then be derived. By modeling spatial correlation with a variogram, we apply these asymptotic results to test independence of two spatially correlated binary outcomes and illustrate the concepts with a well-known example based on data from Lansing Woods. The comparison of generalized estimating equations and the proposed approach is also discussed.Comment: Published at http://dx.doi.org/10.1214/009053605000000057 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org