gev_prob {revdbayes} | R Documentation |
Informative GEV prior on a probability scale
Description
Constructs an informative prior for GEV parameters (\mu, \sigma, \xi
),
constructed on the probability scale. For information about how to set this
prior see set_prior
.
Usage
gev_prob(pars, quant, alpha, min_xi = -Inf, max_xi = Inf, trendsd = 0)
Arguments
pars |
A numeric vector of length 3.
GEV parameters ( |
quant |
A numeric vector of length 3 containing quantiles
( |
alpha |
A numeric vector of length 4. Parameters specifying a
prior distribution for probabilities related to the quantiles in
|
min_xi |
A numeric scalar. Prior lower bound on |
max_xi |
A numeric scalar. Prior upper bound on |
trendsd |
Has no function other than to achieve compatibility with function in the evdbayes package. |
Details
A prior for GEV parameters (\mu, \sigma, \xi)
,
based on Crowder (1992). This construction is typically used to set
an informative prior, based on specified quantiles
q_1, q_2, q_3
.
There are two interpretations of the parameter vector
alpha
= (\alpha_1, \alpha_2, \alpha_3, \alpha_4)
:
as the parameters of beta distributions for ratio of exceedance
probabilities (Stephenson, 2016) and as the parameters of a Dirichlet
distribution for differences between non-exceedance probabilities
(Northrop et al., 2017). See these publications for details.
Value
The log of the prior density.
References
Crowder, M. (1992) Bayesian priors based on parameter transformation using the distribution function Ann. Inst. Statist. Math., 44, 405-416. https://link.springer.com/article/10.1007/BF00050695.
Northrop, P. J., Attalides, N. and Jonathan, P. (2017) Cross-validatory extreme value threshold selection and uncertainty with application to ocean storm severity. Journal of the Royal Statistical Society Series C: Applied Statistics, 66(1), 93-120. doi:10.1111/rssc.12159
Stephenson, A. (2016) Bayesian inference for extreme value modelling. In Extreme Value Modeling and Risk Analysis: Methods and Applications (eds D. K. Dey and J. Yan), 257-280, Chapman and Hall, London. doi:10.1201/b19721.
See Also
set_prior
for setting a prior distribution.
rpost
and rpost_rcpp
for sampling
from an extreme value posterior distribution.
Sets the same prior as the function
prior.prob
in the evdbayes package.