Multivariate models and inference

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Multivariate models that go beyond the assumption of multivariate normality are increasingly being used. Copulas are one tool for constructing multivariate models, and copulas are used in more and more scientific areas. So this area of research is basic scientific research as well as application-motivated. The Web of Science database shows many articles with copula in the title; areas with many copula applications include (i) business, economics and finance, (ii) climate, environment and hydrology, (iii) engineering and reliability, (iv) agriculture, forestry and biostatistics. Any methodology for non-Gaussian dependence will becomes more important with large/huge data sets for which deviations from multivariate normality can be more easily detected.******The extension from multivariate normal models to copula models is typically needed when there is tail dependence or tail asymmetry relative to Gaussian joint tails. In insurance or financial risk analysis, use of classical multivariate normal theory would underestimate risks from jointly large losses.******The main objectives of some recent and proposed future research is to further develop multivariate models and inference/computing procedures for multivariate non-normal response with covariates. With a larger number of variables, it is desirable to have interpretable multivariate models with parsimonious dependence structures and flexible tail behaviour. The various dependence models have interpretations via graphical models which show how different variables are linked and where there are conditional independence relations. Software has been or is being developed to handle very large dimensions. Response types include binary, ordinal categorical, count, survival, heavy-tailed, extreme value. Examples of data include (a) familial data (measurements for each member of an extended multi-generation family) in medical genetics applications, (b) item response data in psychometrics applications, (c) financial asset returns.**