Statistical inference and visualization in scale-space for spatially dependent images

SiZer (SIgnificant ZERo crossing of the derivatives) is a graphical scale-space visualization tool that allows for statistical inferences. In this paper we develop a spatial SiZer for finding significant features and conducting goodness-of-fit tests for spatially dependent images. The spatial SiZer utilizes a family of kernel estimates of the image and provides not only exploratory data analysis but also statistical inference with spatial correlation taken into account. It is also capable of comparing the observed image with a specific null model being tested by adjusting the statistical inference using an assumed covariance structure. Pixel locations having statistically significant differences between the image and a given null model are highlighted by arrows. The spatial SiZer is compared with the existing independent SiZer via the analysis of simulated data with and without signal on both planar and spherical domains. We apply the spatial SiZer method to the decadal temperature change over some regions of the Earth.