den2dCor: den2dCor

In twDEMC: parallel DEMC

Description

Example of log-Unnormalized Density function with changing correlation and scales in variances a ~ N( theta[1], sigmaA ) b ~ N( theta[2], f(a) )

With f(a) exponentially decreasing with increasing a

Usage

den2dCor(theta, muA = 0.8, sigmaA = 1, cb = 1/4, cDen = 0)

Arguments

theta	named numeric vector with components "a" and "b"
muA	parameter for the log-normal distribution of component a
sigmaA
cb	multiplier for density in b
cDen

Author(s)

Thomas Wutzler

Examples

#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]))
head(sort(luden,dec=TRUE))

### 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] ) )

twDEMC documentation built on May 2, 2019, 5:38 p.m.