About the Project
Multivariate response data abound in many application areas including insurance, risk management, finance, biology, psychometrics, health and environmental sciences. Studying associations among multivariate response data is an interesting problem in statistical science. The dependence between random variables is completely described by their multivariate distribution. When the multivariate distribution has a simple form, standard methods can be used to make inference. On the other hand one may create multivariate distributions based on particular assumptions, limiting thus their use. For example, most existing models assume rigid margins of the same form (e.g., Gaussian, Student, exponential, Gamma, Poisson, etc.) and/or limited dependence structure.
To solve this problem copulas seem to be a promising solution. Copulas are a useful way to model multivariate response data, as they account for the dependence structure and provide a flexible representation of the multivariate distribution. The power of copulas for dependence modeling is due to the dependence structure being considered separate from the univariate margins. They allow for flexible dependence modelling, different from assuming simple linear correlation structures and normality; see e.g. Joe (2014). That makes them particularly well suited to many applications in finance, insurance, medicine and psychometrics, among others.
The PhD project will focus on dependence modelling with copulas for non-normal multivariate/longitudinal response data and deal with the development of copula-based,
(a) models with some desirable properties such in Nikoloulopoulos and Joe (2015) and Nikoloulopoulos (2015),
(b) computationally intensive yet tractable estimation methods such in Nikoloulopoulos (2016a,2016b),
with applications in biostatistics, psychometrics, insurance, etc.
Interviews will take place between 16 January and 24 February 2017.
Funding Notes
This PhD project is in a Faculty of Science competition for funded studentships. These studentships are funded for 3 years and comprise home/EU fees, an annual stipend of £14,296 and £1000 per annum to support research training. Overseas applicants may apply but they are required to fund the difference between home/EU and overseas tuition fees (in 2016/17 the difference is £12,879 for the Schools of CHE & PHA, and £9,679 for CMP & MTH but fees are subject to an annual increase).
References
Joe, H. (2014). Dependence Modeling with Copulas. Chapman & Hall, London.
Nikoloulopoulos, A. K. and Joe, H. (2015). Factor copula models for item response data. Psychometrika, 80:126–150.
Nikoloulopoulos, A. K. (2015) A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence. Statistical Methods in Medical Research. DOI: 10.1177/ 0962280215596769.
Nikoloulopoulos, A. K. (2016a) Efficient estimation of high-dimensional multivariate normal copula models with discrete spatial responses. Stochastic Environmental Research and Risk Assessment, 30:493--505.
Nikoloulopoulos, A.K. (2016b) Correlation structure and variable selection in generalized estimating equations via composite likelihood information criteria. Statistics in Medicine, 35:2377--2390.
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