Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flexible models for nonstationary dependence: Methodology and examples   There are many situations when modelling environmental phenomena for which it
is not appropriate to assume a stationary dependence structure.
\cite{sampson1992} proposed an approach to allowing nonstationarity in
dependence based on a deformed space: coordinates from original geographic
"$G$" space are mapped to a new dispersion "$D$" space in which stationary
dependence is a reasonable assumption. \cite{sampson1992} achieve this with two
deformation functions, which are chosen as thin plate splines, each
representing how one of the two coordinates in $D$-space relates to the
original $G$-space coordinates. This works extends the deformation approach,
and the dimension expansion approach of \cite{bornn2012}, to a regression-based
framework in which all dimensions in $D$-space are treated as "smooths" as
found, for example, in generalized additive models. The framework offers an
intuitive and user-friendly approach to specifying $D$-space, allows different
levels of smoothing for dimensions in $D$-space, and allows objective inference
for all model parameters. Furthermore, a numerical approach is proposed to
avoid non-bijective deformations, should they occur, which applies to any
deformation. The proposed framework is demonstrated on the solar radiation data
studied in \cite{sampson1992}, and then on an example related to risk analysis,
which culminates in producing simulations of extreme rainfall for part of
Colorado, US.

24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org