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FRK - Fixed Rank Kriging

A tool for spatial/spatio-temporal modelling and prediction with large datasets. The approach models the field, and hence the covariance function, using a set of basis functions. This fixed-rank basis-function representation facilitates the modelling of big data, and the method naturally allows for non-stationary, anisotropic covariance functions. Discretisation of the spatial domain into so-called basic areal units (BAUs) facilitates the use of observations with varying support (i.e., both point-referenced and areal supports, potentially simultaneously), and prediction over arbitrary user-specified regions. `FRK` also supports inference over various manifolds, including the 2D plane and 3D sphere, and it provides helper functions to model, fit, predict, and plot with relative ease. Version 2.0.0 and above also supports the modelling of non-Gaussian data (e.g., Poisson, binomial, negative-binomial, gamma, and inverse-Gaussian) by employing a generalised linear mixed model (GLMM) framework. Zammit-Mangion and Cressie <doi:10.18637/jss.v098.i04> describe `FRK` in a Gaussian setting, and detail its use of basis functions and BAUs, while Sainsbury-Dale, Zammit-Mangion, and Cressie <doi:10.18637/jss.v108.i10> describe `FRK` in a non-Gaussian setting; two vignettes are available that summarise these papers and provide additional examples.

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8.51 score 76 stars 1 dependents 234 scripts 768 downloads

deepspat - Deep Compositional Spatial Models

Deep compositional spatial models are standard spatial covariance models coupled with an injective warping function of the spatial domain. The warping function is constructed through a composition of multiple elemental injective functions in a deep-learning framework. The package implements two cases for the univariate setting; first, when these warping functions are known up to some weights that need to be estimated, and, second, when the weights in each layer are random. In the multivariate setting only the former case is available. Estimation and inference is done using `tensorflow`, which makes use of graphics processing units. For more details see Zammit-Mangion et al. (2022) <doi:10.1080/01621459.2021.1887741>, Vu et al. (2022) <doi:10.5705/ss.202020.0156>, Vu et al. (2023) <doi:10.1016/j.spasta.2023.100742>, and Shao et al. (2025) <doi:10.48550/arXiv.2505.12548>.

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5.11 score 10 stars 1 scripts 549 downloads

EFDR - Wavelet-Based Enhanced FDR for Detecting Signals from Complete or Incomplete Spatially Aggregated Data

Enhanced False Discovery Rate (EFDR) is a tool to detect anomalies in an image. The image is first transformed into the wavelet domain in order to decorrelate any noise components, following which the coefficients at each resolution are standardised. Statistical tests (in a multiple hypothesis testing setting) are then carried out to find the anomalies. The power of EFDR exceeds that of standard FDR, which would carry out tests on every wavelet coefficient: EFDR choose which wavelets to test based on a criterion described in Shen et al. (2002). The package also provides elementary tools to interpolate spatially irregular data onto a grid of the required size. The work is based on Shen, X., Huang, H.-C., and Cressie, N. 'Nonparametric hypothesis testing for a spatial signal.' Journal of the American Statistical Association 97.460 (2002): 1122-1140.

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4.74 score 5 stars 22 scripts 314 downloads

IDE - Integro-Difference Equation Spatio-Temporal Models

The Integro-Difference Equation model is a linear, dynamical model used to model phenomena that evolve in space and in time; see, for example, Cressie and Wikle (2011, ISBN:978-0-471-69274-4) or Dewar et al. (2009) <doi:10.1109/TSP.2008.2005091>. At the heart of the model is the kernel, which dictates how the process evolves from one time point to the next. Both process and parameter reduction are used to facilitate computation, and spatially-varying kernels are allowed. Data used to estimate the parameters are assumed to be readings of the process corrupted by Gaussian measurement error. Parameters are fitted by maximum likelihood, and estimation is carried out using an evolution algorithm.

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4.70 score 1 stars 9 scripts 272 downloads

sparseinv - Computation of the Sparse Inverse Subset

Creates a wrapper for the 'SuiteSparse' routines that execute the Takahashi equations. These equations compute the elements of the inverse of a sparse matrix at locations where the its Cholesky factor is structurally non-zero. The resulting matrix is known as a sparse inverse subset. Some helper functions are also implemented. Support for spam matrices is currently limited and will be implemented in the future. See Rue and Martino (2007) <doi:10.1016/j.jspi.2006.07.016> and Zammit-Mangion and Rougier (2018) <doi:10.1016/j.csda.2018.02.001> for the application of these equations to statistics.

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4.48 score 1 stars 7 dependents 29 scripts 811 downloads