Mathematical Sciences: Stochastic Modelling and Inference

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Stochastic models and methodologies for statistical inference will be developed in the context of modern instrumentation-intensive experimentation. Bayesian, likelihood- based, semi- and non-parametric methods will be investigated for prediction, calibration, testing and constructing confidence intervals. Efficient and numerically stable computational algorithms will be developed and statistical properties will be investigated both theoretically and via computer experimentation. Much modern science relies on instrumentation-intensive experimentation. With instrument-generated data, the problem may be prediction of responses for new inputs or untried experimental conditions, or calibration of the responses for the test settings, or understanding which components of the response bear a scientific relationship to the input variables. A variety of processes may influence each observed response; the simplest is simple random error, others include deliberate or accidental censoring, and the limitations due the precision of the measuring instrument. Proper, efficient and valuable inferences require statistical models and inferential methodologies with correct understandings of all these processes.