| In this work, we explore spatial statistical models and their potential uses in materials science, with particular emphasis on mean-dependent covariance structures. Materials science, which is the study and design of new solid materials, is a field ripe with complex data that requires sophisticated statistical analysis. We investigate two important materials science data applications: molecular dynamics simulations and crystallography diffraction analysis.;For the molecular dynamics simulations, computer simulations of the three-dimensional atomic structures of materials explore how defects arise under simulated stresses. To overcome the extreme computational burden of these simulations, we develop a spatial statistical model that emulates the final output of these computationally-intensive simulations. In a comparison of multiple spatial regression methods, we find that principal component analysis best predicts defects in the atomic structure.;For the crystallography analysis, radiation diffraction patterns are used to identify the crystal lattice properties of a solid material. We investigate a statistical method of fusing the multiple diffraction data sources to estimate the crystallographic parameters. We determine that variable weighting of the data sources significantly improves the accuracy of the estimates, particularly when parts of the diffraction sources were unreliable due to data corruption.;Finally, as an extension of methods used in the materials sciences analyses, we develop a nonstationary spatial model where the covariance structure is indexed by the mean. Through a simulation study, we explore the inferential and predictive capabilities of the model, showing that it significantly improves upon a stationary spatial model under various circumstances. We then demonstrate these methods on daily precipitation data in Puerto Rico to show how they improve prediction distributions. |
