Nothing
## imprecise/demo/lgamma.R
##
## illustration how to perform the imprecise inferential framework by
## the use of log-gamma imprecise prior on the canonical parameter of
## Poisson model.
##
## 2013.10.21.
library(ipeglim)
rm(list=ls())
## random variates generation from the Poisson with mean 'lambda'
y <- rvg4yx(N=5e1, pars=1, ztrunc=TRUE, xreg=FALSE, kind="pois")$y
table(y)
## model to be fitted
m2fit <- model(formula=y~0, ztrunc=TRUE, dist="pois")
attributes(m2fit)
## model fit with the imprecise prior
## 0.05 <= alpha <= 10
## 0.05 <= beta <= 10
lc0 <- list(lhs=rbind(c(1,0), c(-1,0), c(0,1), c(0,-1)), rhs=c(0.05, -10, 0.05, -10))
cmfit <- impose(obj=m2fit, eqns=lc0)
attributes(cmfit)
## visualization - imprecise prior
## hyperparameter space (M0)
plot(cmfit, xlim=c(-2,12), ylim=c(-2,12),
main="Hyperparameter Space\n constrained by a set of inequalities",
xlab=expression(alpha), ylab=expression(beta))
## output from model fit
op <- update(obj=cmfit, method="LA", apriori="lgamma")
attributes(op)
## summarized output
sop <- summary(op, HT.est=TRUE)
attributes(sop)
## quality check
sop$sratio
## print method
sop
## show the probability box
pbox(x=sop, smooth=TRUE,
main="Probability Box of Canonical Parameter")
pbox(x=sop, which.xtms=c(sop$infs.idx, sop$sups.idx), smooth=TRUE,
main="Probability Box of Canonical Parameter")
## visualization (minimal) - imprecise posterior
z <- range(sop$est)
mar <- 0.5
plot(sop, xlim=c(-2,12), ylim=c(-2,12), zlim=c(z[1]-mar, z[2]+mar),
xlab=list(expression(alpha), cex=1.5, font=1),
ylab=list(expression(beta), cex=1.5, font=1),
zlab=list(expression(E~"("~theta~"|"~y~")"), rot=90, cex=1.5, font=1),
main="Poisson with Imprecise Log-Gamma Prior")
## visualization (on grid) - imprecise prior
cmfit1 <- setGrid(cmfit, len=10)
plot(cmfit1, xlim=c(-2,12), ylim=c(-2,12),
main="Hyperparameter specification",
xlab=expression(alpha), ylab=expression(beta))
## try to change 'method=LA' to 'LA2', 'IS', or 'MH'.
op1 <- update(obj=cmfit1, method="LA", apriori="lgamma")
sop1 <- summary(op1, HT.est=TRUE)
sop1
## visualization (on grid) - imprecise posterior
z <- range(sop$est)
mar <- 0.5
plot(sop1, xlim=c(-2,12), ylim=c(-2,12), zlim=c(z[1]-mar, z[2]+mar),
xlab=list(expression(alpha), cex=1.5, font=1),
ylab=list(expression(beta), cex=1.5, font=1),
zlab=list(expression(E~"("~theta~"|"~y~")"), rot=90, cex=1.5, font=1),
main="Surface of Canonical Parameter\nLog-Gamma Imprecise Prior")
# probability box
pbox(sop1, which.xtms=c(sop1$infs.idx, sop1$sups.idx, 31, 59), smooth=TRUE,
main="Probability Box of Canonical Parameter\non the use of Log-Gamma Imprecise Prior")
## Other imprecise prior specification and its imprecise posterior visualization
bounds <- impose(circle=list(x0=5,y0=5, r=5, len=20))
plot(sop1, bnd=bounds, xlim=c(-2,12), ylim=c(-2,12), zlim=c(z[1]-mar, z[2]+mar),
xlab=list(expression(alpha), cex=1.5, font=1),
ylab=list(expression(beta), cex=1.5, font=1),
zlab=list(expression(E~"("~theta~"|"~y~")"), rot=90, cex=1.5, font=1),
main="Surface of Canonical Parameter\non constratined log-gamma imprecise prior hyperparameter space")
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.