dLogitUnif {nimbleNoBounds}

Logit transformed beta distribution.

Description

Transformation of uniform distribution, via scaled-logit transform, to the real line.

Usage

dLogitUnif(x, min = 0, max = 1, log = 0)

rLogitUnif(n = 1, min = 0, max = 1)

Arguments

x

A continuous random variable on the real line, where y=ilogit(x)*(max-min)+min and y ~ dunif(min, max).

min

lower limit of the distribution. Must be finite.

max

upper limit of the distribution. Must be finite.

log

logical flag. Returns log-density if TRUE.

n

Number of random variables. Currently limited to 1, as is common in nimble. See ?replicate for an alternative.

Value

density, or log-density, of uniform distribution transformed to real line via scaling and logit function.

Author(s)

David R.J. Pleydell

Examples

## Create a uniform random variable, and transform it to the log scale
n      = 100000
lower  = -5
upper  = 11
y      = runif(n=n, lower, upper)
x      = logit((y-lower)/(upper-lower))

## Plot histograms of the two random variables
oldpar <- par()
par(mfrow=n2mfrow(2))
## Plot 1
hist(x, n=100, freq=FALSE)
curve(dLogitUnif(x, lower, upper), -15, 15, n=1001, col="red", add=TRUE, lwd=3)
## Plot 2: back-transformed
xNew = replicate(n=n, rLogitUnif(n=1, lower, upper))
yNew   = ilogit(xNew) * (upper-lower) + lower
hist(yNew, n=100, freq=FALSE, xlab="exp(x)")
curve(dunif(x, lower, upper), -15, 15, n=1001, col="red", lwd=3, add=TRUE)
par(oldpar)

## Create a NIMBLE model that uses this transformed distribution
code = nimbleCode({
  x ~ dLogitUnif(lower, upper)
})


## Build & compile the model
const = list(lower=lower, upper=upper)
modelR = nimbleModel(code=code, const=const)
modelC = compileNimble(modelR)

## Configure, build and compile an MCMC
conf  = configureMCMC(modelC)
mcmc  = buildMCMC(conf=conf)
cMcmc = compileNimble(mcmc)

## Run the MCMC
x = as.vector(runMCMC(mcmc=cMcmc, niter=50000))

## Plot MCMC output
oldpar <- par()
par(mfrow=n2mfrow(3))
## Plot 1: MCMC trajectory
plot(x, typ="l")
## Plot 2: taget density on unbounded sampling scale
hist(x, n=100, freq=FALSE, xlab="x = logit(y)")
curve(dLogitUnif(x, lower, upper), -15, 15, n=1001, col="red", lwd=3, add=TRUE)
## Plot 3: taget density on bounded scale
hist(ilogit(x)*(upper-lower)+lower, n=100, freq=FALSE, xlab="y")
curve(dunif(x, lower, upper), -15, 15, n=1001, col="red", lwd=3, add=TRUE)
par(oldpar)