transOrigPopt.default: transOrigPopt default
In twDEMC: parallel DEMC

Description Usage Arguments Details Value Author(s) See Also Examples

Transform vectors from normal to original scale.

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## Default S3 method:
transOrigPopt(normpopt, poptDistr = parDistr[names(normpopt), 
    "trans"], parDistr, ...)

`normpopt`	numerical vector/array with values at transformed, i.e. normal, scale
`poptDistr`	character vector/array of kind of distribution/transformation (e.g. "norm","lognorm","logitnorm") values with other characters indicate no transformation positions must match the positions in normpopt
`parDistr`	alternative way of specifying poptDistr: dataframe with parameter names in column names and column trans, such as provided by `twQuantiles2Coef`
`...`

Often it is practical to work approximately normally distributed variables and specify mu and sigma parameters. By simple transformations this applied for other distributions as well. For variables strictly greater than zero, the logNormal distribution can be applied. For variables bounded between zero and 1 the logitNormal distribution can be applied.

The values in poptDistr that are currently supported are: "norm", "lognorm", and "logitnorm"

This generic method is provided for in several forms for first argument.

as a named vector: this method
as a matrix: transOrigPopt.matrix
as a coda's mcmc.list: transOrigPopt.mcmc.list
as a list of class twDEMC transOrigPopt.twDEMC

There are further methods deal with parameter transformations.

transforming from original to normal scale: transNormPopt.default
calculating mu and sigma at normal scale from quantiles: twQuantiles2Coef
constraing the result list of twQuantiles2Coef, and adding variance-covariance matrix: twConstrainPoptDistr
calculating the density based on the distribution arguments dDistr

Argument poptDistr should have the same dimensions as normpopt. However, it is recycled. By this way it is possible to specify only one value, or vector corresponding to the rows of a matrix.

Normpopt with some values transformed by exp (poptDist=="lognorm") or plogis (poptDistr=="logitnorm").

Thomas Wutzler

twDEMCBlockInt transNormPopt.default

upperBoundProb = 0.99	# quantile of the upper boundary
parmsBounds = list(		# mode and upper bound
	A0 = c(10,15)		
	,D0 = c(10, 100)
	,C0 = c(0.6,0.8)
)
varDistr <- twVarDistrVec( names(parmsBounds) )	# by default assumed normal
varDistr["D0"] <- "lognorm"
varDistr["C0"] <- "logitnorm"
parDistr <- twQuantiles2Coef( parmsBounds, varDistr, upperBoundProb=upperBoundProb, useMedian=FALSE )
poptDistr <- twConstrainPoptDistr(c("A0","C0"), parDistr)
all.equal( upperBoundProb, pnorm(parmsBounds$A0[2], parDistr[["A0","mu"]], parDistr[["A0","sigmaDiag"]] ) )

# transform entire parameter vectors between scales
pOrig <- transOrigPopt( parDistr$mu, parDistr=parDistr )
# note that transform of mu slighly differs from the mode for lognormal and logitnormal 
pOrig
# back-transform to normal scale
#pBack <- transNormPopt( pOrig, parDistr$trans[names(pOrig)] )	
pBack <- transNormPopt( pOrig, parDistr=parDistr )	
all.equal( parDistr$mu, pBack )

# plot quantiles for given distributions
pGrid <- seq(0.01,0.99,length.out=31)
plot( qnorm(pGrid, mean=parDistr["D0","mu"], sd=parDistr["D0","sigmaDiag"]) ~ pGrid)
plot( qlnorm(pGrid, mean=parDistr["D0","mu"], sd=parDistr["D0","sigmaDiag"]) ~ pGrid); abline(h=parmsBounds[["D0"]][1], col="grey")

# plot densities for D0 parameter ranges
dGrid <- seq(3, 80, length.out=100)
denOrig1 <- dlnorm(dGrid, mean=parDistr["D0","mu"], sd=parDistr["D0","sigmaDiag"]) 
plot( denOrig1 ~ dGrid, type="l"); abline(v=parmsBounds[["D0"]][1], col="grey")

# now plot the same using a grid on normal scale, transforming them to original scale
dNormGrid <- seq( parDistr["D0","mu"]-2*parDistr["D0","sigmaDiag"], parDistr["D0","mu"]+2*parDistr["D0","sigmaDiag"], length.out=100)
dOrigGrid <- transOrigPopt(dNormGrid, parDistr["D0","trans"])
all.equal( dNormGrid, transNormPopt(dOrigGrid, parDistr["D0","trans"]) )
denOrig2 <- dDistr( dOrigGrid, parDistr["D0","mu"],parDistr["D0","sigmaDiag"],trans=parDistr["D0","trans"] )
points( denOrig2 ~ dOrigGrid, col="blue" )