prior {ExtremalDep}

R Documentation

Prior parameter distribution for parametric models.

Description

Random generation from the prior distribution for extremal parametric models or density evaluation of the extremal parametric models.

Usage

	prior(model, type = c("r", "d"), n, par, Hpar, log, dimData)

Arguments

model	The parametric model considered. Values can be model="Pairwise", model="Husler", model="Dirichlet", model="Extremalt" and model="Asymmetric" respectively for the Pairwise Beta, Hulser-Reiss, Tilted Dirichlet, Extremal-t and Asymmetric Logistic.
type	One of the character strings "r" or "d" representing random generation and density of the model considered.
n	The number of parameters to be generated. Only used if type=="r".
par	The values of the parameters. Only used if type=="d". The first elements correspond to the parameters alpha and the last parameters are the beta parameters. See Details.
Hpar	A list of hyper-parameters. See Details.
log	Logical; Only used if type=="d" in order to obtain the log-density. TRUE is the default.
dimData	The dimension of the simplex.

Details

• For the Pairwise Beta model, the parameters components are independent, log-normal. The vector of parameters is of size choose(dim,2)+1 with positive components. The first elements are the pairiwse dependence parameters b and the last one is the global dependence parameter alpha. The list of hyper-parameters should be of the form mean.alpha=, mean.beta=, sd.alpha=, sd.beta=;

• For the Husler-Reiss model, the parameters components are independent, log-normal. The vector of parameters is of size choose(dim,2)+1 with positive components. The elements correspond to the lambda parameter. The list of hyper-parameters should be of the form mean.lambda=, sd.lambda=;

• For the Dirichlet model, the parameters' components are independent, log-normal. The vector of parameters is of size dimData with positive components. The elements correspond to the alpha parameter. The list of hyper-parameters should be of the form mean.alpha=, sd.alpha=;

• For the Extremal-t model, the parameters' components are independent, logit-squared for rho and log-normal for mu. The vector of parameters is of size dimData with positive components. The first elements correspond to the correlation parameters rho and the last parameter is the global dependence parameter mu. The list of hyper-parameters should be of the form mean.rho=, mean.mu=, sd.rho=, sd.mu=;

• For the Asymmetric Logistic model, the parameters' components are independent, log(+1)-normal for alpha and logit for beta. The vector of parameters is of size 2^{dimData-1}(dimData+2)-(2 dimData+1)2^dimData-1(dimData+2)-(2 dimData+1) with positive components. The list of hyper-parameters should be of the form mean.alpha=, mean.beta=, sd.alpha=, sd.beta=.

Value

If type=="r", a matrix with n rows containing a random parameter sample generated under the prior is returned, the (log)-density is returned if type=="d".

Author(s)

Simone Padoan, simone.padoan@unibocconi.it, https://mypage.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com/;

Examples

MCpar <- 0.35
Hpar.pb <- 	list(mean.alpha=0, mean.beta=3,sd.alpha=3, sd.beta=3)
Hpar.hr <- list(mean.lambda=0, sd.lambda=3)
Hpar.di <- list(mean.alpha=0, sd.alpha=3)
Hpar.et <- list(mean.rho=0, mean.mu=3,sd.rho=3, sd.mu=3)
Hpar.alm <- list(mean.alpha=0, mean.beta=0, sd.alpha=3, sd.beta=3)

prior(model="Pairwise", type="r", n=5, Hpar=Hpar.pb, dimData=3)
prior(model="Pairwise", type="d", par=rep(1,choose(4,2)+1), Hpar=Hpar.pb, log=TRUE, dimData=3)

prior(model="Husler", type="r", n=5, Hpar=Hpar.hr, dimData=3)
prior(model="Husler", type="d", par=rep(1,choose(4,2)), Hpar=Hpar.hr, log=TRUE, dimData=3)

prior(model="Dirichlet", type="r", n=5, Hpar=Hpar.di, dimData=3)
prior(model="Dirichlet", type="d", par=rep(1,3), Hpar=Hpar.di, log=TRUE, dimData=3)

prior(model="Extremalt", type="r", n=5, Hpar=Hpar.et, dimData=3)
prior(model="Extremalt", type="d", par=c(rep(0.1,3),4), Hpar=Hpar.et, log=TRUE, dimData=3)

prior(model="Asymmetric", type="r", n=5, Hpar=Hpar.alm, dimData=3)
prior(model="Asymmetric", type="d", par=c(rep(2,4),rep(0.7,9)), Hpar=Hpar.alm, log=TRUE, dimData=3)

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