On univariate and spatial surveillance
Eric Järpe
Ph.D. thesis, Almqvist & Wiksell, 2000.
Abstract
Surveillance methods are needed for detecting a change in
a sequence of random variables, quickly and accurately.
The application determines which models that are appropriate,
and what properties of surveillance methods that are
especially important.
A spatial system is a statistical
model for phenomena occuring in space. In a spatial system, the
distribution of observations made at places in a
geographical region depends on the distance between
these places according to a spatial model. Spatial
surveillance has the aim to detect a change in the
distributions of random variables of a spatial system.
Results on univariate surveillance can sometimes be used in
spatial surveillance.
This thesis contains results on
univariate and spatial surveillance. It is based on three papers.
In Paper I
performance measures of surveillance methods for univariate
monitoring are given for the case when the shift in the mean
of the process differs from that for which the methods are optimised.
Paper II
considers sequential observations of a spatial system. The spatial
model is an auto-logistic model (known as the Ising model), and
the focus is on surveillance of the interaction parameter in it.
A univariate minimal sufficient statistic is derived. This
statistic has simple asymptotic properties and univariate
surveillance may be conducted. Some general methods of
surveillance can be used. This is illustrated by examples.
The results of Paper I are applicable to the results of
this study.
In Paper
III the focus is on detection
of environmental catastrophes. A harmful increase of the
level, of some substance, that spreads with e.g. the wind,
is considered. For the situation of no spread,
it is possible to use previous studies on univariate and
multivariate surveillance. Different
kinds of spreading scenarios are discussed and treated.
Methods for detecting the shift taking the spread into
account, are suggested. A brief evaluation of these methods
is made. An application to radiation data for detecting an
increase in radiation, is considered. The method used today
is compared to some alternative ones.