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- W4287903118 abstract "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." @default.
- W4287903118 created "2022-07-26" @default.
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- W4287903118 date "2020-01-18" @default.
- W4287903118 modified "2023-09-26" @default.
- W4287903118 title "Flexible models for nonstationary dependence: Methodology and examples" @default.
- W4287903118 doi "https://doi.org/10.48550/arxiv.2001.06642" @default.
- W4287903118 hasPublicationYear "2020" @default.
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