Outlier-Robust Surrogate Modeling of Ion-Solid Interaction Simulations.

Data for complex plasma-wall interactions require long-running and expensive computer simulations. Furthermore, the number of input parameters is large, which results in low coverage of the (physical) parameter space. Unpredictable occasions of outliers create a need to conduct the exploration of this multi-dimensional space using robust analysis tools. We restate the Gaussian process (GP) method as a Bayesian adaptive exploration method for establishing surrogate surfaces in the variables of interest. On this basis, we expand the analysis by the Student-t process (TP) method in order to improve the robustness of the result with respect to outliers. The most obvious difference between both methods shows up in the marginal likelihood for the hyperparameters of the covariance function, where the TP method features a broader marginal probability distribution in the presence of outliers. Eventually, we provide first investigations, with a mixture likelihood of two Gaussians within a Gaussian process ansatz for describing either outlier or non-outlier behavior. The parameters of the two Gaussians are set such that the mixture likelihood resembles the shape of a Student-t likelihood.

Familial recurrence risk with varying amount of family history.

The familial recurrence risk is the probability a person will have disease, given a reported family history. When family histories are obtained as simple counts of disease among family members, as often obtained in cancer registries or surveys, we propose methods to estimate recurrence risks based on truncated binomial distributions. By this approach, we are able to obtain unbiased estimates of risk for a person with at least k-affected relatives, where k can be specified to determine how risk varies with k. We also derive robust variances of the recurrence risk estimate, to account for correlations within families, such as those induced by shared genes or shared environment, without explicitly modeling the factors that cause familial correlations. Furthermore, we illustrate how mixture models can be used to account for a sample composed of low- and high-risk families. Using simulations, we illustrate the properties of the proposed methods. Application of our methods to a family history survey of prostate cancer shows that the recurrence risk for prostate cancer increased from 16%, when there was at least one affected relative, to 52%, when there was at least five affected relatives.