Abstract This thesis presents methods for modelling conditional variance and uncertainty of prediction at a query point on the basis of industrial process data. The introductory part of the thesis provides an extensive background of the examined methods and a summary of the results. The results are presented in detail in the original papers. The application presented in the thesis is modelling of the mean and variance of the mechanical properties of steel plates. Both the mean and variance of the mechanical properties depend on many process variables. A method for predicting the probability of rejection in a quali?cation test is presented and implemented in a tool developed for the planning of strength margins. The developed tool has been successfully utilised in the planning of mechanical properties in a steel plate mill. The methods for modelling the dependence of conditional variance on input variables are reviewed and their suitability for large industrial data sets are examined. In a comparative study, neural network modelling of the mean and dispersion narrowly performed the best. A method is presented for evaluating the uncertainty of regression-type prediction at a query point on the basis of predicted conditional variance, model variance and the effect of uncertainty about explanatory variables at early process stages. A method for measuring the uncertainty of prediction on the basis of the density of the data around the query point is proposed. The proposed distance measure is utilised in comparing the generalisation ability of models. The generalisation properties of the most important regression learning methods are studied and the results indicate that local methods and quadratic regression have a poor interpolation capability compared with multi-layer perceptron and Gaussian kernel support vector regression. The possibility of adaptively modelling a time-varying conditional variance function is disclosed. Two methods for adaptive modelling of the variance function are proposed. The background of the developed adaptive variance modelling methods is presented.

<p>Advancements in human genomic technology have helped to improve our understanding of how genetic variation plays a central role in the mechanism of disease susceptibility. However, the very high dimensional nature of the data generated from large-scale genetic association studies has limited our ability to thoroughly examine genetic interactions. A prioritization scheme – Variance Prioritization (VP) – has been developed to select genetic variants based on differences in the quantitative trait variance between the possible genotypes using Levene’s test (Pare et al., 2010). Genetic variants with Levene’s test p-values lower than a pre-determined level of significance are selected to test for interactions using linear regression models. Under a variety of scenarios, VP has increased power to detect interactions over an exhaustive search as a result of reduced search space. Nevertheless, the use of Levene’s test does not take into account that the variance will either monotonically increase or decrease with the number of minor alleles when interactions are present. To address this issue, I propose a maximum likelihood approach to test for trends in variance between the genotypes, and derive a closed-form representation of the likelihood ratio test (LRT) statistic. Using simulations, I examine the performance of LRT in assessing the inequality of quantitative traits variance stratified by genotypes, and subsequently in identifying potentially interacting genetic variants. LRT is also used in an empirical dataset of 2,161 individuals to prioritize genetic variants for gene-environment interactions. The interaction p-values of the prioritized genetic variants are consistently lower than expected by chance compared to the non-prioritized, suggesting improved statistical power to detect interactions in the set of prioritized genetic variants. This new statistical test is expected to complement the existing VP framework and accelerate the process of genetic interaction discovery in future genome-wide studies and meta-analyses.</p> / Master of Health Sciences (MSc)