Semiparametric bivariate modelling with flexible extremal dependence

Inference over multivariate tails often requires a number of assumptions which may affect the assessment of the extreme dependence structure. Models are usually constructed in such a way that extreme components can either be asymptotically dependent or be independent of each other. Recently, there has been an increasing interest on modelling multivariate extremes more flexibly, by allowing models to bridge both asymptotic dependence regimes. Here we propose a novel semiparametric approach which allows for a variety of dependence patterns, be them extremal or not, by using in a model-based fashion the full dataset. We build on previous work for inference on marginal exceedances over a high, unknown threshold, by combining it with flexible, semiparametric copula specifications to investigate extreme dependence, thus separately modelling marginals and dependence structure. Because of the generality of our approach, bivariate problems are investigated here due to computational challenges, but multivariate extensions are readily available. Empirical results suggest that our approach can provide sound uncertainty statements about the possibility of asymptotic independence, and we propose a criterion to quantify the presence of either extreme regime which performs well in our applications when compared to others available. Estimation of functions of interest for extremes is performed via MCMC algorithms. Attention is also devoted to the prediction of new extreme observations. Our approach is evaluated through simulations, applied to real data and assessed against competing approaches. Evidence demonstrates that the bulk of the data do not bias and improve the inferential process for extremal dependence in our applications

Dynamic analysis of survival models and related processes.

This thesis presents new methods of analysis of survival data based on a Dynamic Bayesian approach. The models allow the parameters to change with time. The analysis is tractable and emphasises predictive aspects of the models. The survival problems covered include linear and non-linear regression, analysis of random samples, time-dependent covariates, life tables and competing risks. The analysis is also extended to a number of point processes. Numerical applications are provided and the microcomputer software to perform them is described

State space models with spatial deformation

Space deformation has been proposed to model space-time varying observation processes with non-stationary spatial covariance structure under the hypothesis of temporal stationarity. In real applications, however, the temporal stationarity assumption is inappropriate and unrealistic. In thisworkwe propose a spatialtemporal model whose temporal trend is modeled through state space models and a spatially varying anisotropy is modeled through spatial deformation, under the Bayesian approach. A distinctive feature of our approach is the consideration of model uncertainty in an unified framework. Our model has a clear advantage over the ones proposed so far in the literature when themain objective of the study is to perform spatial interpolation for fixed points in time. Approximations of the posterior distributions of the model parameters are obtained via Markov chain Monte Carlo methods. This allows for prediction of the process values in space and time as well as handling of missing values. Two applications are presented: the first one to model concentrations of sulfur dioxide in the eastern United States and the second one to model monthly minimum temperatures in the State of Rio de Janeiro

Análise bayesiana do funcionamento diferencial do item

This paper uses a Bayesian approach for parameter estimation in Item Response Theory Models for DIF – Differential Item Functioning – analysis. The models proposed are integrated, and incorporate regression structures that can be used to explain the DIF related to items associated covariates. The models are proposed for multiple groups and the approach used, naturally, consider the estimation error of the latent trace and the estimation error of the structural parameters. Examples with simulated data and real data are also presented.Neste trabalho utiliza-se a abordagem Bayesiana na estimação dos parâmetros de modelos da Teoria da Resposta ao Item, destinados à análise do Funcionamento Diferencial do Item, DIF – Differential Item Functioning. Os modelos propostos são integrados, e permitem incorporar estruturas de regressão que podem ser usadas para explicar o DIF relacionado à co-variáveis associadas aos itens. São considerados modelos para múltiplos grupos e a abordagem utilizada incorpora naturalmente o erro de estimação do traço latente e dos parâmetros estruturais. A abordagem permite, naturalmente, considerar DIF tanto na dificuldade quanto na discriminação do item. Exemplos com dados simulados e com dados reais são apresentados