The ability to find regions where a stochastic process exceeds a certain level, or is significantly different from some reference level, is important in several areas of application. A related problem is uncertainty quantification of contour curves and more generally of contour maps, which are often used to display estimates of continuous surfaces. The number of contours used in a contour map should typically reflect the uncertainty in the estimate, since one should be allowed to draw many contours if the uncertainty of the estimated surface is low and fewer contours if the uncertainty is high. The ability to quantify the uncertainty in the contour map is important if one should be able to choose the number of contours in a rigorous way.
excursions contains functions for solving these problems for latent Gaussian models (LGMs), which is a large model class that is widely used in applications. The computational methods are especially well-suited for models where the latent field has Markov properties. Solving the problems involves computing high-dimensional Gaussian integrals, which can be done more efficiently if Markov properties can be utilized. With the ability to efficiently compute Gaussian integrals, one can also compute simultaneous credible bands for latent Gaussian processes, and more generally for mixtures of Gaussian processes.
The package supports at least three ways of specifying the model that should be analyzed. The standard method for purely Gaussian models is to specify the model by providing the parameters of the Gaussian process. For more general models, the input can either be given as Monte Carlo simulations of the process or as the result from an analysis using the R-INLA or inlabru packages.
See the Getting started vignette for an introduction to the main functions of the package. A complete list of functions is contained in the excursions documentation and a brief introduction to the theory is provided in the Methodology vignette.
The INLA interface is introduced in the R-INLA vignette and the inlabru interface is introduced in the inlabru vignette.
Installation instructions
The latest CRAN release of the package can be installed directly from CRAN with install.packages("excursions"). The latest stable version (which is sometimes slightly more recent than the CRAN version), can be installed by using the command
remotes::install_github("davidbolin/excursions", ref = "stable")in R. The development version can be installed using the command
remotes::install_github("davidbolin/excursions", ref = "devel")