Archive | 2021
Visualization of Joint Spatio-temporal Models via Feature Recognition with an Application to Wildland Fires
Abstract
Many spatial statistics applications result in a collection of spatial estimates, especially if a different (but possibly correlated) estimate is produced for a sequence of time epochs. For a small collection of epochs, the connections or trends between estimates and the prominent or common features can be found via inspection of the spatial estimates. As the number of spatial estimates grows, this task becomes much more difficult. We present a method of summarizing a sequence of estimates using an image recognition technique called NonNegative Matrix Factorization which results in a meaningful decomposition of the source images into basis functions and coefficients. This visualization technique allows for investigation of trends over time as well as common spatial features of the estimates without needing to fit a temporal model or use pre-specified spatial regions. We apply this technique to a sequence of models that jointly model the spatial location of wildland fires with the total burn area of each of the fires. We discuss the extensions of the visualization technique to the joint modelling framework and are able to draw new insights about the connection between the location and size of the fires.