Prediction distribution is the basis for many predictive inferences. Unlike the common practice of estimating parameters of a model or performing tests of hypotheses regarding the parameters involved, often the aim of a researcher/practitioner is to predict the value of a (or a set of) future response(s) from a given model. The technique of prediction is used in many real world situations as it has common sense appeal and simple interpretation. The prediction distribution is the probability distribution of one or more future (unobserved) responses, conditional on a set of observed responses from the same model. The method is useful in both univariate and multivariate problems. Predictive inference is possible for models with independent as well as dependent and correlated responses. Bayesian and other approaches are adopted for the purpose of predictive inference. Available methods can handle the conventional normal model and non-normal robust models. Application of predictive inference includes problems in areas such as tolerance regions, model selection, process control, optimisation, perturbation and many others. The customary use of the normal model comes under serious question when the population distribution is symmetric but have heavier tails that the normal distribution. Also, the normal model fails to incorporate dependent but uncorrelated responses. In such cases the multivariate Student-t distribution provides an appropriate model for the population. For such models we can obtain the maximum likelihood estimators of the mean and scale parameters of multivariate Student-t distribution. The model has been used to find appropriate test statistic to test the mean vector. The distributions of the sum of squares and product matrix for the multivariate Student-t model as well as the predictive distribution of future model have been proposed. Similar results for the matrix T and elliptically contoured model are also obtained. Both classical and Bayesian approaches can be applied. Projects in this area will extend this previous work.

Professor Shahjahan Khan

• Dr Trevor Langlands

• School of Agricultural and Environmental Sciences

• Other Medical and Health Sciences
• Statistics

• Doctor of Philosophy (DPHD)
• Master of Research (MRES)