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
