Contributions to parametric statistical theory and practice

Published work (twenty research papers and two books) and two unpublished papers are presented within the context of a short commentary on the theme of statistical parametric modelling. A secondary theme is the stimulus brought to statistical theory through close attention to the requirements of particular practical problems. The developments discussed cover the main divisions of parametric modelling: model selection, model validity, estimation, hypothesis testing, experimental design, prediction, decision making, model fitting and complex modelling. In model selection and validity the presentation begins and ends with an intensive study of two important particular classes of models, the centenarian lognormal class and a new logistic-normal class with wide application in the analysis of compositional and probabilistic data. In estimation and hypothesis testing the main aim is the provision of routine methodology, to allow the basy consideration of non-standard and complex situations. The discussion includes multiple hypothesis testing problems, in particular the usq of restricted and confidence-region tests, and a problem of constructing optimum designs for certain comparative trials. The emergence of statistical prediction analysis and the central role of predictive distributions as an important tool in many practical situations, with advantages of realism and tractability over other methods, are explained. The necessary theory for applications in medicine, in particular to statistical diagnosis, is developed, and the more complex models required to take account of difficulties of calibration, imprecision and uncertain diagnoses are constructed. Methods of comparing human inferential judgment against statistical modelling are demonstrated, and the possibility of estimating the implicit utility functions used by clinicians in their allocations of treatments to patients is explored.