[R] initial points for arms in package HI

[Christoph Buser]

Dear R-users

I have a problem choosing initial points for the function arms()
in the package HI
I intend to implement a Gibbs sampler and one of my conditional
distributions is nonstandard and not logconcave.
Therefore I'd like to use arms.

But there seem to be a strong influence of the initial point
y.start. To show the effect I constructed a demonstration
example. It is reproducible without further information.  

Please note that my target density is not logconcave.

Thanks for all comments or ideas.

Christoph Buser

## R Code:

library(HI)
## parameter for the distribution
para <- 0.1

## logdensity
logDichteGam <- function(x, u = para, v = para) {
  -(u*x + v*1/x) - log(x)
}
## density except for the constant
propDichteGam <- function(x, u = para, v = para) {
  exp(-(u*x + v*1/x) - log(x))
}
## calculating the constant 
(c <- integrate(propDichteGam, 0, 1000, rel.tol = 10^(-12))$value)
## density
DichteGam <- function(x, u = para, v = para) {
  exp(-(u*x + v*1/x) - log(x))/c
}

## calculating 1000 values by repeating a call of arms (this would
## be the situation in an Gibbs Sample. Of course in a Gibbs sampler
## the distribution would change. This is only for demonstration
res1 <- NULL
for(i in 1:1000)
  res1[i] <- arms(runif(1,0,100), logDichteGam, function(x) (x>0)&(x<100), 1)

## Generating a sample of thousand observations with 1 call of arms
res2 <- arms(runif(1,0,100), logDichteGam, function(x) (x>0)&(x<100), 1000)

## Plot of the samples 
mult.fig(4)
plot(res1, log = "y")
plot(res2, log = "y")
hist(res1, freq = FALSE, xlim = c(0,4), breaks = seq(0,100,by = 0.1),
     ylim = c(0,1))
curve(DichteGam, 0,4, add = TRUE, col = 2)
hist(res2, freq = FALSE, xlim = c(0,4), breaks = seq(0,100,by = 0.1),
     ylim = c(0,1))
curve(DichteGam, 0,4, add = TRUE, col = 2)


## If we repeat the procedure, using the fix intial value 1,
## the situation is even worse
res3 <- NULL
for(i in 1:1000)
  res3[i] <- arms(1, logDichteGam, function(x) (x>0)&(x<100), 1)

## Generating a sample of thousand observations with 1 call of arms
res4 <- arms(1, logDichteGam, function(x) (x>0)&(x<100), 1000)

## Plot of the samples 
par(mfrow = c(2,2))
plot(res3, log = "y")
plot(res4, log = "y")
hist(res3, freq = FALSE, xlim = c(0,4), breaks = seq(0,100,by = 0.1),
     ylim = c(0,1))
curve(DichteGam, 0,4, add = TRUE, col = 2)
hist(res4, freq = FALSE, xlim = c(0,4), breaks = seq(0,100,by = 0.1),
     ylim = c(0,1))
curve(DichteGam, 0,4, add = TRUE, col = 2)


## If I generate the sample in a for-loop (one by one) I do not
## get the correct density. But this is exactly the situation in 
## my Gibbs Sampler. Therfore I am concerned about the correct 
## application of arms

--------------------------------------------------------------
Christoph Buser <buser at stat.math.ethz.ch>
Seminar fuer Statistik, LEO C13
ETH (Federal Inst. Technology)	8092 Zurich	 SWITZERLAND
phone: x-41-44-632-4673		fax: 632-1228
http://stat.ethz.ch/~buser/