On Wednesday 25th March 2020, the Department of Mathematical Sciences at Durham University will hold a Lecture Day on Recent Developments in Copula Research. The event is supported by the London Mathematical Society (LMS) Celebrating New Appointments Scheme. The programme for the meeting is shown below; the venue will be the Department of Mathematical Sciences, Durham University (marked 15 on the map). Further Travel Information can be found here.
There is no registration fee, but for catering purposes please let us know by Wednesday 4th of March if you would like to attend. To confirm attendance, or in case of any questions, please contact Tahani Coolen-Maturi (tahani.maturi@durham.ac.uk).
We develop factor copula models for analysing the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric and non-linear dependence. They can be explained as conditional independence models with latent variables that don't necessarily have an additive latent structure. We focus on important issues that would interest the social data analyst, such as model selection and goodness-of-fit. Our general methodology is demonstrated with an extensive simulation study and illustrated by re-analysing three mixed response datasets. Our study suggests that there can be a substantial improvement over the standard factor model for mixed data and makes the argument for moving to factor copula models.
A new method is presented for prediction of an event involving a future bivariate observation. The method combines nonparametric predictive inference (NPI) applied to the marginals with a (non)parametric copula to model and estimate the dependence structure between two random quantities. In NPI, uncertainty is quantified through imprecise probabilities. Several novel aspects of statistical inference are presented. First, the link between NPI and copulas is powerful and attractive with regard to computation. Secondly, statistical methods using imprecise probability have gained substantial attention in recent years, where typically imprecision is used on aspects for which less information is available. A different approach, namely imprecision mainly being introduced on the marginals, is presented for which there is typically quite sufficient information, in order to provide robustness for the harder part of the inference, namely the dependence structure. Thirdly, the set-up of the simulations to evaluate the performance of the proposed method is novel, key to these are frequentist comparisons of the success proportion of predictions with the corresponding data-based lower and upper predictive inferences. All these novel ideas can be applied far more generally to other inferences and models.