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.
gev_prob(pars, quant, alpha, min_xi = -Inf, max_xi = Inf, trendsd = 0)A numeric vector of length 3. GEV parameters (\(\mu, \sigma, \xi\)).
A numeric vector of length 3 containing quantiles
(\(q_1, q_2, q_3\)) such that
\(q_1 < q_2 < q_3\). If the values
in quant are not ordered from smallest to largest then they
will be ordered inside set_prior without warning.
A numeric vector of length 4. Parameters specifying a
prior distribution for probabilities related to the quantiles in
quant. See Details below.
A numeric scalar. Prior lower bound on \(\xi\).
A numeric scalar. Prior upper bound on \(\xi\).
Has no function other than to achieve compatibility with function in the evdbayes package.
The log of the prior density.
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.
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 .
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.