Preface
Spatial analysis methods have seen a rapid rise in popularity due to demand from a
wide range of fields. These include, among others, biology, spatial economics, im-
age processing, environmental and earth science, ecology, geography, epidemiology,
agronomy, forestry and mineral prospection.
In spatial problems, observations come from a spatial process X = {X
s
, s ∈ S}
indexed by a spatial set S, with X
s
taking values in a state space E. The positions
of observation sites s ∈ S are either fixed in advance or random. Classically, S is a
2-dimensional subset, S ⊆R
2
. However, it could also be 1-dimensional (chromatog-
raphy, crop trials along rows) or a subset of R
3
(mineral prospection, earth science,
3D imaging). Other fields such as Bayesian statistics and simulation may even re-
quire spaces S of dimension d ≥ 3. The study of spatial dynamics adds a temporal
dimension, for example (s,t) ∈ R
2
×R
+
in the 2-dimensional case.
This multitude of situations and applications makes f or a very rich subject. To
illustrate, let us give a few examples of the three types of spatial data that will be
studied in the book.
Geostatistical data
Here, S is a continuous subspace of R
d
and the random field {X
s
, s ∈ S} observed
at n fixed sites {s
1
,...,s
n
}⊂S takes values in a real-valued state space E.The
rainfall data in Figure 0.1-a and soil porosity data in Fig. 0.1-b fall into this cate-
gory. Observation sites may or may not be regularly spaced. Geostatistics tries to
answer questions about modeling, identification and separation of small and large
scale variations, prediction (or kriging) at unobserved sites and reconstruction of X
across the whole space S.
Lattice data and data on fixed networks
Here, S is a fixed discrete non-random set, usually S ⊂ R
d
and X is observed at
points in S. Points s might be geographical regions represented as a network with
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