Density of the proposal distribution q(cur.par,prop.par) and random generator for MCMC algorithm in the NL3 model.
proposal.nl(
type = c("r", "d"),
cur.par,
prop.par,
MCpar = get("nl.MCpar"),
log = TRUE
)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".
One of the character strings "r" or "d".
Current state of the chain.
Candidate parameter.
A list made of a single element: MCMC parameter. Re-centering parameter for the proposal distribution.
Logical. Only used when type =="d". Should the result be returned on the log-scale ?
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.