Abstract

The spatial component of a space-time random field
is (a) a low dimensional vector, (b) a high dimensional vector,
or (c) a subset of Euclidean space. The local signals are
(i) jump changes, (ii) slope changes, or (iii) bubbles. Specific
cases of interest are (a) the local signal appears
simultaneously in all coordinges, (b) the signal appears
in a (relatively small) subset of the coordinates, and
(c) the signal is defined by a spatially and temporally limited
kernel. Our goal is to detect these local signal(s), taking appropriate
account of multiple comparisons, and estimate their location and
spatial extent. Examples include (A) COVID-SARS2 in wastewater,
(B) hate crimes in the US tracked by the FBI, (C) temperature
anomalies, (D) excess deaths during the recent pandemic.