The investigators will apply process convolution modeling techniques to non-stationary data in new ways. Convolutions are used both for their theoretical elegance and their computational efficiency. The first focus is on the spatio-temporal setting, with exploration of different approaches to applying convolutions to the problem. Both theoretical and implementational aspects will be addressed. The second focus is on partitioned processes, starting in the spatial setting and moving on to spatio-temporal problems. Partitioning is a computationally effective method for dealing with non-stationarity, and combined with the convolution approach allows for practical modeling of much larger datasets than can traditionally be analyzed with a non-stationary model.
This work is on new statistical models for processes that vary over distance and time, possibly varying in an irregular fashion. Motivating examples come from environmental science (such as understanding rainfall and other environmental variables, and validating computer models for climate simulations) and aeronautical engineering (modeling of computational fluid dynamics simulators, such as flight simulators). Such complex processes can be difficult to model well, as complicated models can be too difficult to use while simpler models fail to fit well. This work involves models which are sufficiently powerful, yet also practical to use for larger datasets. Success will impact not just the realm of statistical modeling, but more importantly will help advance research in the fields of the applications, in particular environmetrics and aeronautical engineering.
