Mathematical Sciences: New Methodology for Predictive Inference

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A non-parametric approach is developed to select models for categorical and survival data, with a view to helping the elicitation of predictors and prognostic factors. The tests put forward take the form of central limit theorems for normalized scoring functions. The sequential aspect of the data collection is taken into account. The goal of the research is to establish sound theoretical foundations for these diagnostics and to demonstrate their practicality. For survival models, the distributional properties of residuals from the probability integral transform conditional on sufficient statistics will also be studied. In the event that these properties are easily characterized, conditions, under which a sequential application of the transformation leads to a test of predictive validity of the model, will be sought. The construction of empirical Bayes confidence intervals based on structured priors is set in a predictive framework and will be addressed via both analytical methods and bootstrap samples. Comparison with respect to several validation criteria will discriminate between existing and proposed techniques. Focussing on observables, the characteristics of prediction intervals based on empirical Bayes distributions will be looked into. A novel approach for the selection models for categorical and survival data, is developed. This methodology will help in the elicitation of predictors and prognostic factors. The sequential aspect of the data collection is taken into account. The goal of the research is to establish sound theoretical foundations for these diagnostics and to demonstrate their practicality. The construction of empirical Bayes confidence intervals based on structured priors in a predictive framework. The construction of these intervals will be addressed via both analytical methods and bootstrap samples. Comparison with respect to several validation criteria will discriminate between existing and proposed techniques. Focussing on observables, t he characteristics of prediction intervals based on empirical Bayes distributions will be looked into.