Developments in Wishart ensemble and Bayesian application

Abstract

The increased complexity and dimensionality of data necessitates the development of new models that can adequately model the data. Advances in computational approaches have pathed the way for consideration and implementation of more complicated models, previously avoided due to practical difficulties. New models within theWishart ensemble are developed and some properties are derived. Algorithms for the practical implementation of these matrix variate models are proposed. Simulation studies and real datasets are used to illustrate the use and improved performance of these new models in Bayesian analysis of the multivariate and univariate normal models. From this speculative research study the following papers emanated: 1. J. Van Niekerk, A. Bekker, M. Arashi, and J.J.J. Roux (2015). “Subjective Bayesian analysis of the elliptical model”. In: Communications in Statistics - Theory and Methods 44.17, 3738–3753 2. J. Van Niekerk, A. Bekker, M. Arashi, and D.J. De Waal (2016). “Estimation under the matrix variate elliptical model”. In: South African Statistical Journal 50.1, 149–171 3. J. Van Niekerk, A. Bekker, and M. Arashi (2016). “A gamma-mixture class of distributions with Bayesian application”. In: Communications in Statistics - Simulation and Computation (Accepted) 4. M. Arashi, A. Bekker, and J. Van Niekerk (2017). “Weighted-type Wishart distributions with application”. In: Revstat 15(2), 205–222 5. A. Bekker, J. Van Niekerk, and M. Arashi (2017). “Wishart distributions - Advances in Theory with Bayesian application”. In: Journal of Multivariate Analysis 155, 272–283