censoredLikelihoodBR {mvPot}

Censored log-likelihood function for the Brown–Resnick model.

Description

Compute the peaks-over-threshold censored negative log-likelihood function for the Brown–Resnick model.

Usage

censoredLikelihoodBR(
  obs,
  loc,
  vario,
  u,
  p = 499L,
  vec = NULL,
  nCores = 1L,
  cl = NULL,
  likelihood = "mgp",
  ntot = NULL,
  ...
)

censoredLikelihood(
  obs,
  loc,
  vario,
  u,
  p = 499L,
  vec = NULL,
  nCores = 1L,
  cl = NULL
)

Arguments

obs

List of vectors for which at least one component exceeds a high threshold.

loc

Matrix of coordinates as given by expand.grid().

vario

Semi-variogram function taking a vector of coordinates as input.

u

Vector of threshold under which to censor components.

p

Number of samples used for quasi-Monte Carlo estimation. Must be a prime number.

vec

Generating vector for the quasi-Monte Carlo procedure. For a given prime p and dimension, can be computed using genVecQMC.

nCores

Number of cores used for the computation

cl

Cluster instance as created by makeCluster of the parallel package.

likelihood

vector of strings specifying the contribution. Either "mgp" for multivariate generalized Pareto, "poisson" for a Poisson contribution for the observations falling below or "binom" for a binomial contribution.

ntot

integer number of observations below and above the threshold, to be used with Poisson or binomial likelihood

...

Additional arguments passed to Cpp routine.

Details

The function computes the censored negative log-likelihood function based on the representation developed by Wadsworth et al. (2014) and Engelke et al. (2015). Margins must have been standardized first, for instance to the unit Frechet scale.

Value

Negative censored log-likelihood for the set of observations obs and semi-variogram vario with attributes exponentMeasure for all of the likelihood type selected, in the order "mgp", "poisson", "binom".

Author(s)

Raphael de Fondeville

References

Wadsworth, J. L. and J. A. Tawn (2014). Efficient inference for spatial extreme value processes associated to log-Gaussian random functions. Biometrika, 101(1), 1-15.

Asadi, P., Davison A. C. and S. Engelke (2015). Extremes on River Networks. Annals of Applied Statistics, 9(4), 2023-2050.

Examples

#Define semi-variogram function
vario <- function(h){
   0.5 * norm(h, type = "2")^1.5
}

#Define locations
loc <- expand.grid(1:4, 1:4)

#Simulate data
obs <- simulPareto(1000, loc, vario)

#Evaluate risk functional
maxima <- sapply(obs, max)
thres <- quantile(maxima, 0.9)

#Select exceedances
exceedances <- obs[maxima > thres]

#Compute generating vector
p <- 499
latticeRule <- genVecQMC(p, (nrow(loc) - 1))
primeP <- latticeRule$primeP
vec <- latticeRule$genVec


#Compute log-likelihood function
censoredLikelihoodBR(obs = exceedances, loc = loc, vario = vario,
 u = thres, p = primeP, vec = vec, ntot = 1000)