Prior simulation of GEV parameters - prior on quantile scale

Simulates from the prior distribution for GEV parameters proposed in Coles and Tawn (1996), based on independent gamma priors for differences between quantiles.

rprior_quant(n, prob, shape, scale, lb = NULL, lb_prob = 0.001)

Arguments

n

A numeric scalar. The size of sample required.

prob

A numeric vector of length 3. Exceedance probabilities corresponding to the quantiles used to specify the prior distribution. The values should decrease with the index of the vector. If not, the values in prob will be sorted into decreasing order without warning.

shape

A numeric vector of length 3. Respective shape parameters of the gamma priors for the quantile differences.

scale

A numeric vector of length 3. Respective scale parameters of the gamma priors for the quantile differences.

lb

A numeric scalar. If this is not NULL then the simulation is constrained so that lb is an approximate lower bound on the GEV variable. Specifically, only simulated GEV parameter values for which the 100lb_prob% quantile is greater than lb are retained.

lb_prob

A numeric scalar. The non-exceedance probability involved in the specification of lb. Must be in (0,1). If lb=NULL then lb_prob is not used.

Value

An n by 3 numeric matrix.

Details

The simulation is based on the way that the prior is constructed. See Coles and Tawn (1996), Stephenson (2016) or the evdbayes user guide for details of the construction of the prior. First, the quantile differences are simulated from the specified gamma distributions. Then the simulated quantiles are calculated. Then the GEV location, scale and shape parameters that give these quantile values are found, by solving numerically a set of three non-linear equations in which the GEV quantile function evaluated at the values in prob is equated to the simulated quantiles. This is reduced to a one-dimensional optimisation over the GEV shape parameter.

References

Coles, S. G. and Tawn, J. A. (1996) A Bayesian analysis of extreme rainfall data. Appl. Statist., 45, 463-478.

Stephenson, A. 2016. Bayesian Inference for Extreme Value Modelling. In Extreme Value Modeling and Risk Analysis: Methods and Applications, edited by D. K. Dey and J. Yan, 257-80. London: Chapman and Hall. doi:10.1201/b19721

See also

rpost and rpost_rcpp for sampling from an extreme value posterior distribution.

Examples

pr <- 10 ^ -(1:3)
sh <- c(38.9, 7.1, 47)
sc <- c(1.5, 6.3, 2.6)
x <- rprior_quant(n = 1000, prob = pr, shape = sh, scale = sc)
x <- rprior_quant(n = 1000, prob = pr, shape = sh, scale = sc, lb = 0)