Informative GEV prior on a probability scale

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 (\(\mu, \sigma, \xi\)).
quant: 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.
alpha: A numeric vector of length 4. Parameters specifying a prior distribution for probabilities related to the quantiles in quant. See Details below.
min_xi: A numeric scalar. Prior lower bound on \(\xi\).
max_xi: A numeric scalar. Prior upper bound on \(\xi\).
trendsd: Has no function other than to achieve compatibility with function in the evdbayes package.

Value

The log of the prior density.

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.

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 .