A copula is a multivariate model whose marginals are uniform. A copula based model is one that is based on a copula. The attraction of using copula models is that we can separately model the marginal distributions and the dependence structure of our target distribution. Such models are particularly attractive when some or all of the marginals are discrete or a mixture of discrete and continuous components. A multivariate probit model is one simple example of a copula model.
In the last decade or so, there has been a dramatic increase in storage facilities and the possibility of processing huge amounts of data. This has made large high-quality data sets widely accessible for practitioners. This technology innovation seriously challenges inference methodology, in particular simulation algorithms commonly applied in Bayesian inference. These algorithms typically require repeated evaluations over the whole data set when fitting models, precluding their use in the age of so called big data.
This project pursues breakthroughs which allow important questions of basic and applied science to be addressed using mathematical decision models. Advances are made through an interdisciplinary effort, combining recent developments in econometric and statistical methods, cognitive science, and advances in computing. The outcomes will bring to a new range of questions a proven and powerful approach for investigating psychological effects. The project will begin this expansion effort with investigations of choices about health care and consumer purchases.
Tran, M N., Nott D., Kuk A., & Kohn R.
(2016). Parallel variational Bayes for large datasets with an application to generalized linear mixed models. Journal of Computational and Graphical Statistics. 25(2), 626-646. doi: 10.1080/10618600.2015.1012293