gev_prob: Informative GEV prior on a probability scale

In paulnorthrop/revdbayes: Ratio-of-Uniforms Sampling for Bayesian Extreme Value Analysis

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 (\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.

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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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.

paulnorthrop/revdbayes documentation built on March 20, 2024, 1:01 a.m.