Cationic copolymerization of cycloaliphatic epoxy resin with a spirobislactone with lanthanum triflate as initiator: I. Characterization and shrinkage

3,4‐Epoxycyclohexylmethyl 3,4‐epoxycyclohexane carboxylate (ECH) was cured with different proportions of 1,6‐dioxaspiro [4,4]nonane‐2,7‐dione (s(γ‐BL)) using lanthanum triflate as a catalyst. The shrinkage undergone during curing was monitored by means of thermomechanical analysis (TMA) in isothermal experiments. Fourier transform infrared spectroscopy in attenuated‐total‐reflection mode (FTIR/ATR) was used to study the evolution of lactone, epoxide, and intermediate spiroorthoester (SOE) groups to identify the different reactions that take place during the curing process. DSC was used to study the thermal characteristics of the curing process and to assess the glass‐transition temperature (T_g) of the cured material. The dynamic mechanical properties of the cured material were determined based on the data obtained by DMTA. An increase in the proportion of s(γ‐BL) led to a decrease in the gelation time and the shrinkage after gelation. By combining the data obtained by TMA and FTIR/ATR, it was also possible to identify the reactive processes responsible for the shrinkage. It was observed that an increase in the proportion of s(γ‐BL) also increases the speed of the curing process and modifies the structure of the material, thus giving rise to more flexible materials. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3421–3432, 2005     

Bayesian analysis of constant elasticity of variance models

This paper focuses on the estimation of some models in finance and in particular, in interest rates. We analyse discretized versions of the constant elasticity of variance (CEV) models where the normal law showing up in the usual discretization of the diffusion part is replaced by a range of heavy‐tailed distributions. A further extension of the model is to allow the elasticity of variance to be a parameter itself. This generalized model allows great flexibility in modelling and simplifies the model implementation considerably using the scale mixtures representation. The mixing parameters provide a means to identify possible outliers and protect inference by down‐weighting the distorting effects of these outliers. For parameter estimation, Bayesian approach is adopted and implemented using the software WinBUGS (Bayesian inference using Gibbs sampler). Results from a real data analysis show that an exponential power distribution with a random shape parameter, which is highly leptokurtic compared with the normal distribution, forms the best CEV model for the data. Copyright © 2006 John Wiley & Sons, Ltd.     

Bayesian analysis of lymphatic spreading patterns in cancer of the thoracic esophagus

For the treatment of patients with cancer of the thoracic esophagus, lymphatic spreading is one important factor to infer how advanced their cancer is. We introduced a one-dimensional scale based on lymphatic spreading patterns, the stage of cancer, to express how advanced their cancer is, and we proposed a method to infer each patient's stage from his lymphatic spreading pattern by applying a Bayesian model. Our Bayesian model was built based on the assumption that lymphatic spreading in cancer could be explained as what was brought about by the advance of stage. In the modeling, we introduced the probability of what stage each patient was in as a prior distribution. We also introduced distribution functions of Weibull distributions to express the relation between the advance of stage and the increase of the probability of metastasis. Our model was applied to the data of nodal involvement obtained from 103 patients with cancer of the thoracic esophagus and the parameters were estimated with the maximum likelihood method. AIC was used to check that the data had enough information to be divided into the stages of a clinically reasonable number. With the estimated parameters, we inferred the probability of metastasis to each lymph node in each stage and calculated by Bayes' theorem with 31 new patients the probability of what stage they were in. The results well represented some characteristics of the lymphatic spreading and suggested the appropriateness of our approach.The present study was carried out under the ISM Cooperative Research Program (91-ISM·CRP-18).     

基于统计滤波的单幅散斑条纹图的相位恢复技术

基于统计信号处理技术的贝叶斯（Bayes）估计原理，提出一种新的滤波方法。该方法能有效减少散斑条纹图中的噪声，而且仅用一幅散区斑条纹图就能获得准确的条纹相位分布，通过实例说明了该方法的处理过程。     

稀土对ZA27合金底缩影响的机制

研究了金属镧和铈基混合稀土对凝固速率为３２℃／ｍｉｎ的ＺＡ２７底缩的影响。结果表明，Ｌａ和混合稀土均使ＺＡ２７底缩体积和总缩孔体积减小；二者加入量大于０３％时，底部缩孔封闭，内部缩孔位置逐渐上移。稀土化合物下沉富集在试样底部，是造成底部缩孔封闭的原因。由于稀土的加入不能有效地阻止α初生相的上浮，内部缩孔位置仍靠近试样底部。     

Algebraic geometry of Gaussian Bayesian networks

Conditional independence models in the Gaussian case are algebraic varieties in the cone of positive definite covariance matrices. We study these varieties in the case of Bayesian networks, with a view towards generalizing the recursive factorization theorem to situations with hidden variables. In the case when the underlying graph is a tree, we show that the vanishing ideal of the model is generated by the conditional independence statements implied by graph. We also show that the ideal of any Bayesian network is homogeneous with respect to a multigrading induced by a collection of upstream random variables. This has a number of important consequences for hidden variable models. Finally, we relate the ideals of Bayesian networks to a number of classical constructions in algebraic geometry including toric degenerations of the Grassmannian, matrix Schubert varieties, and secant varieties.     

Computation of reference Bayesian inference for variance components in longitudinal studies

Generalized linear mixed models (GLMMs) have been applied widely in the analysis of longitudinal data. This model confers two important advantages, namely, the flexibility to include random effects and the ability to make inference about complex covariances. In practice, however, the inference of variance components can be a difficult task due to the complexity of the model itself and the dimensionality of the covariance matrix of random effects. Here we first discuss for GLMMs the relation between Bayesian posterior estimates and penalized quasi-likelihood (PQL) estimates, based on the generalization of Harville’s result for general linear models. Next, we perform fully Bayesian analyses for the random covariance matrix using three different reference priors, two with Jeffreys’ priors derived from approximate likelihoods and one with the approximate uniform shrinkage prior. Computations are carried out via the combination of asymptotic approximations and Markov chain Monte Carlo methods. Under the criterion of the squared Euclidean norm, we compare the performances of Bayesian estimates of variance components with that of PQL estimates when the responses are non-normal, and with that of the restricted maximum likelihood (REML) estimates when data are assumed normal. Three applications and simulations of binary, normal, and count responses with multiple random effects and of small sample sizes are illustrated. The analyses examine the differences in estimation performance when the covariance structure is complex, and demonstrate the equivalence between PQL and the posterior modes when the former can be derived. The results also show that the Bayesian approach, particularly under the approximate Jeffreys’ priors, outperforms other procedures.     

Bayesian networks with a logistic regression model for the conditional probabilities

Logistic regression techniques can be used to restrict the conditional probabilities of a Bayesian network for discrete variables. More specifically, each variable of the network can be modeled through a logistic regression model, in which the parents of the variable define the covariates. When all main effects and interactions between the parent variables are incorporated as covariates, the conditional probabilities are estimated without restrictions, as in a traditional Bayesian network. By incorporating interaction terms up to a specific order only, the number of parameters can be drastically reduced. Furthermore, ordered logistic regression can be used when the categories of a variable are ordered, resulting in even more parsimonious models. Parameters are estimated by a modified junction tree algorithm. The approach is illustrated with the Alarm network.     

An optimization-based approach for the design of Bayesian networks

Bayesian networks model conditional dependencies among the domain variables, and provide a way to deduce their interrelationships as well as a method for the classification of new instances. One of the most challenging problems in using Bayesian networks, in the absence of a domain expert who can dictate the model, is inducing the structure of the network from a large, multivariate data set. We propose a new methodology for the design of the structure of a Bayesian network based on concepts of graph theory and nonlinear integer optimization techniques.     

Bayesian parameter inference for models of the Black and Scholes type

In this paper, we describe a general method for constructing the posterior distribution of the mean and volatility of the return of an asset satisfying dS=SdX for some simple models of X. Our framework takes as inputs the prior distributions of the parameters of the stochastic process followed by the underlying, as well as the likelihood function implied by the observed price history for the underlying. As an application of our framework, we compute the value at risk (VaR) and conditional VaR (CVaR) measures for the changes in the price of an option implied by the posterior distribution of the volatility of the underlying. The implied VaR and CVaR are more conservative than their classical counterpart, since it takes into account the estimation risk that arises due to parameter uncertainty. Copyright © 2008 John Wiley & Sons, Ltd.