proposal.nl: NL3 model: proposal distribution.

In lbelzile/BMAmevt: Multivariate Extremes: Bayesian Estimation of the Spectral Measure

NL3 model: proposal distribution.

Description

Density of the proposal distribution q(cur.par,prop.par) and random generator for MCMC algorithm in the NL3 model.

Usage

proposal.nl(
  type = c("r", "d"),
  cur.par,
  prop.par,
  MCpar = get("nl.MCpar"),
  log = TRUE
)

Arguments

type	One of the character strings "r" or "d".
cur.par	Current state of the chain.
prop.par	Candidate parameter.
MCpar	A list made of a single element: MCMC parameter. Re-centering parameter for the proposal distribution.
log	Logical. Only used when type =="d". Should the result be returned on the log-scale ?

Details

The two components of proposal parameter (alpha*, beta12*, beta13*, beta23*) are generated independently, under a beta distribution with mode at the current parameter's value.

Let \epsilon = MCpar$eps.recentre. To generate alpha*, given the current state alpha(t), let m(t) = \epsilon /2 + (1-\epsilon) * \alpha(t) be the mean of the Beta proposal distribution and \lambda = 2/\epsilon (a scaling constant). Then

\alpha^* \sim \textrm{Beta}(\lambda m(t), (1-\lambda) m(t))

The betaij*'s are generated similarly.

Value

Either the (log-)density of the proposal parameter prop.par, given cur.par (if type == "d"), or a proposal parameter (a vector), if type =="r".

lbelzile/BMAmevt documentation built on April 28, 2023, 2:29 p.m.