A Statistical Approach to Spatial Mapping of Temperature Change

In this thesis, spatio-temporal temperature trends are estimated based on monthly average temperatures from 503 observation locations in the southern half of Norway. The time period studied is 1960 to 2016. A latent Gaussian model is proposed, where spatial Gaussian random fields and temporal polynomials of second degree are used to model the temperature trends. A Bayesian approach is taken for the inference, and the integrated nested Laplace approximations methodology is used to carry out the inference. The model is easy to interpret, has interpretable results, is able to predict missing observations, and successfully estimates temperature trends that correspond to other research results. Five sets of different prior distributions are used on the model components, each month of the year is modelled individually, and all months have the same prior distributions for each set of priors. In general, the temperature trend is increasing over the entire southern half of Norway according to the model, and the five sets of prior distributions give similar results. Twelve different spatio-temporal temperature trends, one for each month of the year, are obtained, and all months of the year have experienced an increase in temperature from 1960 to 2016. In some areas and some months, the temperature has decreased as well. The increase is largest during the winter months, and smallest during the summer months. The model is computationally fast; the inference is carried out in approximately 20 minutes for each month. The range parameters of the Gaussian random fields are given extra attention, and a minor prior sensitivity analysis on the range parameters is carried out. The sensitivity analysis reveals that to achieve the interpretable results, the range parameters, especially for the warmest months of the year, must to a large extent be controlled by the prior distribution

Robust Modelling of Additive and Non-additive Variation with Intuitive Inclusion of Expert Knowledge

We propose a novel Bayesian approach that robustifies genomic modeling by leveraging expert knowledge (EK) through prior distributions. The central component is the hierarchical decomposition of phenotypic variation into additive and nonadditive genetic variation, which leads to an intuitive model parameterization that can be visualized as a tree. The edges of the tree represent ratios of variances, for example broad-sense heritability, which are quantities for which EK is natural to exist. Penalized complexity priors are defined for all edges of the tree in a bottom-up procedure that respects the model structure and incorporates EK through all levels. We investigate models with different sources of variation and compare the performance of different priors implementing varying amounts of EK in the context of plant breeding. A simulation study shows that the proposed priors implementing EK improve the robustness of genomic modeling and the selection of the genetically best individuals in a breeding program. We observe this improvement in both variety selection on genetic values and parent selection on additive values; the variety selection benefited the most. In a real case study, EK increases phenotype prediction accuracy for cases in which the standard maximum likelihood approach did not find optimal estimates for the variance components. Finally, we discuss the importance of EK priors for genomic modeling and breeding, and point to future research areas of easy-to-use and parsimonious priors in genomic modeling