Copula models have become increasingly popular for modeling multivariate survival data. In this paper we review some of the recent work that has been appeared for copula model for bivariate survival data and propose a Bayesian modeling. Our approach is very flexible with respect to the choice of marginal distributions and, depending on the copula model employed, it is possible to have a class of variation for the dependence parameter. We compare some of the copula models using a descriptive diagnostic method and three popular Bayesian model selection criteria. Our methodology is illustrated with the Diabetic Retinopathy Study (1976).

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We study patterns of the phase diagram of ferromagnetic Ising models on graphs under an external magnetic field. We provide an example of a tree with only two types of vertices on which for a range of values of the external field there is a unique Gibbs distribution at low enough and at high enough temperatures, while at intermediate temperatures there is phase coexistence (in other words, a reentrance transition takes place).

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