dgaps_post {revdbayes} | R Documentation |
Random sampling from D-gaps posterior distribution
Description
Uses the rust
package to simulate from the posterior
distribution of the extremal index based on the D-gaps model
for threshold interexceedance times of Holesovsky and Fusek (2020). We refer
to this as the
-gaps model, because it uses a tuning parameter
, whereas the related
-gaps model of Suveges and Davison
(2010) has a tuning parameter
.
Usage
dgaps_post(
data,
thresh,
D = 1,
n = 1000,
inc_cens = TRUE,
alpha = 1,
beta = 1,
param = c("logit", "theta"),
use_rcpp = TRUE
)
Arguments
data |
A numeric vector or numeric matrix of raw data. If If |
thresh |
A numeric scalar. Extreme value threshold applied to data. |
D |
A numeric scalar. The censoring parameter |
n |
A numeric scalar. The size of posterior sample required. |
inc_cens |
A logical scalar indicating whether or not to include
contributions from right-censored inter-exceedance times, relating to the
first and last observations. It is known that these times are greater
than or equal to the time observed.
If |
alpha , beta |
Positive numeric scalars. Parameters of a
beta( |
param |
A character scalar. If |
use_rcpp |
A logical scalar. If |
Details
A beta(,
) prior distribution is used for
so that the posterior from which values are simulated is
proportional to
See dgaps_stat
for a description of the variables
involved in the contribution of the likelihood to this expression.
The ru
function in the rust
package simulates from this posterior distribution using the
generalised ratio-of-uniforms distribution. To improve the probability
of acceptance, and to ensure that the simulation will work even in
extreme cases where the posterior density of is unbounded as
approaches 0 or 1, we simulate from the posterior
distribution of
and then transform back to the
-scale.
Value
An object (list) of class "evpost"
, which has the same
structure as an object of class "ru"
returned from
ru
.
In addition this list contains
-
call
: The call todgaps()
. -
model
: The character scalar"dgaps"
. -
thresh
: The argumentthresh
. -
ss
: The sufficient statistics for the D-gaps likelihood, as calculated bydgaps_stat
.
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
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
See Also
ru
for the form of the object returned by
dgaps_post
.
kgaps_post
for Bayesian inference about the
extremal index using the
-gaps model.
Examples
# Newlyn sea surges
thresh <- quantile(newlyn, probs = 0.90)
d_postsim <- dgaps_post(newlyn, thresh)
plot(d_postsim)
### Cheeseboro wind gusts
d_postsim <- dgaps_post(exdex::cheeseboro, thresh = 45, D = 3)
plot(d_postsim)