revdbayes: Ratio-of-Uniforms Sampling for Bayesian Extreme Value Analysis

Uses the multivariate generalized ratio-of-uniforms method to simulate random samples from the posterior distributions commonly encountered in Bayesian extreme value analyses.

Details

The main functions in the revdbayes package are rpost and rpost_rcpp, which simulate random samples from the posterior distribution of extreme value model parameters using the functions ru and ru_rcpp from the rust package, respectively. The user chooses the extreme value model, the prior density for the parameters and provides the data. There are options to improve the probability of acceptance of the ratio-of-uniforms algorithm by working with transformation of the model parameters.

The functions kgaps_post and dgaps_post simulate from the posterior distribution of the extremal index \(\theta\) based on the K-gaps model for threshold interexceedance times of Suveges and Davison (2010) and the similar D-gaps model of Holesovsky and Fusek (2020). See also Attalides (2015).

See vignette("revdbayes-a-vignette", package = "revdbayes") for an overview of the package and vignette("revdbayes-b-using-rcpp-vignette", package = "revdbayes") for an illustration of the improvements in efficiency produced using the Rcpp package. See vignette("revdbayes-c-predictive-vignette", package = "revdbayes") for an outline of how to use revdbayes to perform posterior predictive extreme value inference and vignette("revdbayes-d-kgaps-vignette", package = "revdbayes") considers Bayesian inference for the extremal index \(\theta\) using threshold inter-exceedance times.

References

Holesovsky, J. and Fusek, M. Estimation of the extremal index using censored distributions. Extremes 23, 197-213 (2020). doi:10.1007/s10687-020-00374-3

Northrop, P. J. (2016). rust: Ratio-of-Uniforms Simulation with Transformation. R package version 1.2.2. https://cran.r-project.org/package=rust.

Suveges, M. and Davison, A. C. (2010) Model misspecification in peaks over threshold analysis, The Annals of Applied Statistics, 4(1), 203-221. doi:10.1214/09-AOAS292

Attalides, N. (2015) Threshold-based extreme value modelling, PhD thesis, University College London. https://discovery.ucl.ac.uk/1471121/1/Nicolas_Attalides_Thesis.pdf

See also

set_prior to set a prior density for extreme value parameters.

rpost and rpost_rcpp to perform ratio-of-uniforms sampling from an extreme value posterior distribution.

kgaps_post and dgaps_post to sample from a posterior distribution for the extremal index based on inter-exceedance times.

The ru and ru_rcpp functions in the rust package for details of the arguments that can be passed to ru via rpost and for the form of the object (of class "evpost") returned from rpost, which has the same structure as an object (of class "ru") returned by ru and ru_rcpp.