proposal {ExtremalDep} | R Documentation |
Density of the proposal distribution q(cur.par, prop.par)
and
random generator of the MCMC algorithm for parametric models.
proposal(model, type = c("r", "d"), cur.par, prop.par, MCpar, log = TRUE)
model |
The parametric model considered. Values can be |
type |
One of the character strings "r" or "d" representing random generation and density for the Asymmetric Logistic model. |
cur.par |
Vector representing the current state of the chain. See Details. |
prop.par |
Vector representing the candidate parameters. See Details. |
MCpar |
A list made of a single element: MC MC parameter. Re-centering parameters for the proposal distribution. |
log |
Logical; Only used if |
For the Pairwise Beta model
, cur.par
and prop.par
are of size choose(dim,2)+1
.
The components prop.par[i]
of the proposal distribution are generated independently from
the log-normal distribution.
prop.par = rlnorm(length(cur.par), meanlog=log(cur.par), sdlog = rep(MCpar$sdlog, length(cur.par)))
;
For the Husler-Reiss model
, cur.par
and prop.par
are of size choose(dim,2)
.
The components prop.par[i]
of the proposal distribution are generated independently from
the log-normal distribution.
prop.par = rlnorm(length(cur.par), meanlog=log(cur.par), sdlog = rep(MCpar$sdlog, length(cur.par)))
;
For the Tilted Dirichlet model, cur.par
and prop.par
are of size dim
.
The components prop.par[i]
of the proposal distribution are generated independently from
the log-normal distribution.
prop.par = rlnorm(length(cur.par), meanlog=log(cur.par), sdlog = rep(MCpar$sdlog, length(cur.par)))
;
For the Extremal-t model, cur.par
and prop.par
are of size choose(dim,2)+1
.
The components prop.par[i]
of the proposal distribution are generated independently from
the square root of an inverse logit transformation of the normal distribution for the correlation
parameters rho
and from the log transformation of the normal distribution for the global dependence
parameter (the degreee of freedom mu
);
For the Asymmetric Logistic model, cur.par
and prop.par
are
of size 2^{d-1}(d+2)-(2d-1)
.
The components prop.par[i]
of the proposal distribution are generated independently from
the log transformation of the normal distribution (minus 1) for the parameters alpha
and from the inverse logit transformation of the parameters beta
;
Either the (log)-density of the proposal prop.par
, given cur.par
(if type=="d"
)
or a proposal parameter (a vector), if type=="r".
Simone Padoan, simone.padoan@unibocconi.it, https://mypage.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com/;
proposal("Pairwise", "r", rep(1,4), MCpar=0.35)
proposal("Pairwise", "d", rep(1,4), rep(1.2,4), MCpar=0.35)
proposal("Husler", "r", rep(1,4), MCpar=0.35)
proposal("Husler", "d", rep(1,4), c(1.2,4), MCpar=0.35)
proposal("Dirichlet", "r", rep(1,3), MCpar=0.35)
proposal("Dirichlet", "d", rep(1,3), c(1.2,3), MCpar=0.35)
proposal("Extremalt", "r", rep(0.5,3), MCpar=0.35)
proposal("Extremalt", "d", c(rep(0.9,3),3), c(rep(0.8,3),2), MCpar=0.35)
proposal("Asymmetric", "r", c(rep(1.1,4),rep(0.1,9)), MCpar=0.35)
proposal("Asymmetric", "d", c(rep(1.1,4),rep(0.1,9)), c(rep(1.2,4),rep(0.1,9)), 0.35)