Professor Mardia's main research contributions broadly span the following seven areas of statistics:
Much of his research in these areas has been motivated by challenging and new emerging applications in a wide variety of fields including
He has continued to lead the field of Statistics of Manifolds throughout his career which includes directional data and shape analysis. The problems on manifolds are not straightforward and his achievements in this field include his own path-breaking research, its cutting edge applications (such as in proteins as their function and evolution, Fetal Alcohol Damage Syndrome) and creating a community in the research area.
Additionally, his work in Kriging, warping methods, multivariate measure of skewness and kurtosis are some other of his landmark contributions. Further highlights are as follows.
1. Statistics on Manifolds
Directional Statistics: Research Monograph, RSS Discussion paper, Mardia
model on Torus, Line finding statistical procedure.
Shape Analysis: Mardia-Dryden model, Goodall-Mardia multivariate shape models, Bilateral symmetry and projective invariants. Research Monograph. Shape of brain and FASD.
Statistical Bioinformatics: Alignment through Bayesian hierarchical model, directional hidden Markov models for local structure prediction of protein (PNAS paper).
2. Linear Statistics
Multivariate Analysis: Mardia's measure of skewness and kurtosis, Multivariate MRF, Book
Spatial Statistics: Maximum likelihood estimation in Kriging and of Kriging with derivative information.
Statistical Image Analysis: Fusion methods, segmentation methods, warping methods. RSS Discussion paper.
Spatial Temporal Modelling: Kriged-Kalman filter. TEST discussion paper.
Indeed, Mardia's research has been guided by his mission statement for the Leeds Annual Statistical Research Workshops:
"Statistics without science is incomplete,
Science without statistics is imperfect."