# R/den2dCor.R In twDEMC: parallel DEMC

#### Documented in den2dCor

```den2dCor <- function(
### Example of log-Unnormalized Density function with changing correlation and scales in variances
theta	##<< named numeric vector with components "a" and "b"
,muA=0.8,sigmaA=1	##<< parameter for the log-normal distribution of component a
,cb=1/4	##<< multiplier for density in b
#,cb=1e-900	##<< multiplier for density in b
,cDen=0
){
##description<<
## a ~ N( theta[1], sigmaA )
## b ~ N( theta[2], f(a) )
##
## With f(a) exponentially decreasing with increasing a
#
a <- theta[1]
b <- theta[2]
lda <- ((a-muA)/sigmaA)^2
sdb <- exp(-2.8*a)*80
mub <- (0.8-a)^2*20
ldb <- ((b-mub)/sdb)^2
#-1/2 * ( lda + max(ldb,0.9*lda))  # may not be a density
c( den = as.numeric(-1/2 * ( lda + ldb )) )			   # also not a density because sigmab depends on a and does not factor out
}
attr(den2dCor,"ex") <- function(){
#gridlogx <- seq(log(0.1),log(+4),length.out=91)
#gridx <- exp(gridlogx)
gridx <- a <- seq(-0.5,2,length.out=91)
#plot( lda ~ a)
gridy <- seq(-20,+40,length.out=91)
gridX <- expand.grid(gridx, gridy)
den2dCor(c(0.8,0.8))
luden <- apply( gridX, 1, den2dCor )
mLuden <- matrix(luden,nrow=length(gridx))
#plot( rowSums(mLuden) ~ gridx )
imax <- which( matrix(luden,nrow=length(gridx))==max(luden), arr.ind=TRUE)
#c( gridx[ imax[1] ], gridy[ imax[2] ] )

image( gridx, gridy,  mLuden, col = rev(heat.colors(100)), xlab="a", ylab="b" )
xyMax <- c(x=gridx[ imax[1] ], y=gridy[ imax[2] ])

image( gridx, gridy,  matrix(exp(luden),nrow=length(gridx)), col = rev(heat.colors(100)), xlab="a", ylab="b" )
points( gridx[ imax[1] ], gridy[ imax[2] ]  )

q20 <- quantile(luden,0.2)
plot(density(luden[luden>q20]))

### todo: normalizing constant:

##------------------ do an MCMC run
(.expTheta <- c(a=0,b=0) )
(.expCovTheta <- diag(c(a=2,b=2)) )
.nPop=2
Zinit <- initZtwDEMCNormal( .expTheta, .expCovTheta, nChainPop=4, nPop=.nPop)
#mtrace(twDEMCBlockInt)

den2dCorTwDEMC <- twDEMCBlock(Zinit, nGen=500, dInfos=list(d1=list(fLogDen=den2dCor)), nPop=.nPop )
den2dCorTwDEMC <- twDEMCBlock(den2dCorTwDEMC, nGen=1000)

plot( thinN(as.mcmc.list(den2dCorTwDEMC)))
matplot( concatPops(den2dCorTwDEMC)\$pAccept[,1,], type="l" )
pps <- pps0 <- stackChains(thin(den2dCorTwDEMC,start=300))
ss <- ss0 <- pps[,-1]
#plot( ss[,1], ss[,2] )
plot( ss[,1], ss[,2], ylim=c(-40,80) )
plot( density(ss[,1]) )
plot( ecdf( ss[,1] ) )
plot( ecdf( ss[,2] ) )
}
```

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twDEMC documentation built on May 31, 2017, 3:44 a.m.