ExtremeRisks (version 0.0.5)

extBQuantx: Conditional Bayesian extreme quantile

Description

Given posterior samples for the parameters of the continuous or discrete generalized Pareto distribution and scedasis function for a set of covariates, return the posterior mean and \(1-\alpha\) level credibility intervals of the extreme quantile for each value of the scedasis function

Usage

extBQuantx(
  cx,
  postsamp,
  threshold,
  n,
  qlev,
  k,
  type = c("continuous", "discrete"),
  confint = c("asymmetric", "symmetric"),
  alpha = 0.05,
  ...
)

Value

a list with components

• mQ posterior mean of the extreme quantile

• ciQ vector of dimension 2 returning the \(\alpha/2\) and \(1-\alpha/2\) empirical quantiles of the posterior distribution of the extreme quantile

Arguments

cx

an m by p matrix, obtained by evaluating the scedasis function for every of the p covariate values and every m posterior draw

postsamp

a m by 2 matrix with columns containing the posterior samples of scale and shape parameters of the generalized Pareto distribution, respectively

threshold

threshold for the generalized Pareto model, corresponding to the \(n-k\)th order statistic of the sample

n

integer, number of observations in the full sample. Must be greater than k

qlev

double indicating the percentile level at which the extreme quantile is estimated. Must be smaller than \(k/n\)

k

integer, number of exceedances for the generalized Pareto (only used if extrapolation=TRUE)

type

string indicating distribution types. Default: c('continuous','discrete')

confint

type of confidence interval. Default: c('asymmetric', 'symmetric')

alpha

level for credibility interval. Default 0.05, giving 95% credibility intervals

...

additional arguments, for back-compatilibity

Examples

if (FALSE) {
# generate data
set.seed(1234)
n <- 500
samp <- evd::rfrechet(n,0,1:n,4)
# set effective sample size and threshold
k <- 50
threshold <- sort(samp,decreasing = TRUE)[k+1]
# preliminary mle estimates of scale and shape parameters
mlest <- evd::fpot(
  samp,
  threshold,
  control = list(maxit = 500))
# empirical bayes procedure
proc <- estPOT(
  samp,
  k = k,
  pn = c(0.01, 0.005),
  type = "continuous",
  method = "bayesian",
  prior = "empirical",
  start = as.list(mlest$estimate),
  sig0 = 0.1)
# conditional predictive density estimation
yg <- seq(0, 50, by = 2)
nyg <- length(yg)
# estimation of scedasis function
# setting
M <- 1e3
C <- 5
alpha <- 0.05
bw <- .5
nsim <- 5000
burn <- 1000
# create covariate
# in sample obs
n_in = n
# number of years ahead
nY = 1
n_out = 365 * nY
# total obs
n_tot = n_in + n_out
# total covariate (in+out sample period)
x <- seq(0, 1, length = n_tot)
# in sample grid dimension for covariate
ng_in <- 150
xg <- seq(0, x[n_in], length = ng_in)
# in+out of sample grid
xg <- c(xg, seq(x[n_in + 1], x[(n_tot)], length = ng_in))
# in+out sample grid dimension
nxg <- length(xg)
xg <- array(xg, c(nxg, 1))
# in sample observations
samp_in <- samp[1:n_in]
ssamp_in <- sort(samp_in, decreasing = TRUE, index = TRUE)
x_in <- x[1:n_in] # in sample covariate
xs <- x_in[ssamp_in$ix[1:k]] # in sample concomitant covariate
# estimate scedasis function over the in and out of sample period
res_stat <- apply(
  xg,
  1,
  cpost_stat,
  N = nsim - burn,
  x = x_in,
  xs = xs,
  bw = bw,
  k = k,
  C = C
)
# conditional predictive posterior density
probq = 1 - 0.99
res_AQ <- extBQuantx(
 cx = res_stat,
 postsamp = proc$post_sample,
 threshold = proc$t,
 n = n,
 qlev = probq,
 k = k,
 type = "continuous",
 confint = "asymmetric")
 }