DRclass_lu_Pdf {DRclass}R Documentation

Calculate marginal class bounding functions for the general case of a Density Ratio Class.

Description

See the function 'DRclass_k_Pdf' for the case in which the upper and lower bounding functions of the class are proportional.

Usage

DRclass_lu_Pdf(sample_u, l, u, nout = 512, ...)

Arguments

sample_u

Sample from a distribution proportional to the upper bound of the class, often from the posterior of the upper bound of the prior in Bayesian inference. Columns represent variables, rows go across the sample.

l

Either a function to evaluate the lower bound of the Density Ratio Class or a vector of values of this function evaluated for the rows of 'sample_u'. Note that in the context of Bayesian inference the upper bound of the prior can be provided as only the ratio of l/u is needed and the likelihood cancels in this fraction. This saves computation time as the prior is usually computationally much cheaper to evaluate than the likelihood.

u

Either a function to evaluate the upper bound of the Density Ratio Class or a vector of values of this function evaluated for the rows of 'sample_u'. Note that in the context of Bayesian inference the lower bound of the prior can be provided as only the ratio of l/u is needed and the likelihood cancels in this fraction. This saves computation time as the prior is usually computationally much cheaper to evaluate than the likelihood.

nout

Number of equally spaced output intervals for the marginal densities.

...

Further arguments passed to the function 'density'

Value

Three dimensional array with the following dimensions: 1: variable corresponding to column of the sample 2: equidistant spacing of that variable 3: three columns for variable values, upper normalized density of the marginal class, lower non-normalized density of the marginal class

Examples

# example of the application of DRclass functions:
# ------------------------------------------------

# parameter values
k        <- 10
sd       <- 0.5
sampsize <- 10000

# upper and lower class boundaries:
u <- function(x) { return(    dnorm(x,0,sd)) }
l <- function(x) { return(1/k*dnorm(x,0,sd)) }

# generate sample:
sample_u <- cbind(rnorm(sampsize,0,sd),rnorm(sampsize,0,sd))  # example of 2d sample

# get class boundaries (back from sample):
pdf1   <- DRclass_k_Pdf(sample_u,k=k,adjust=2)       # faster for l proportional to u
pdf2   <- DRclass_lu_Pdf(sample_u,l=l,u=u,adjust=2)  # l and u could have different shapes

# get cdf bounds:
cdf1   <- DRclass_k_Cdf(sample_u,k=k)
cdf2   <- DRclass_lu_Cdf(sample_u,l=l,u=u)

# get quantile bounds:
quant1 <- DRclass_k_Quantile(sample_u,k=k,probs=c(0.025,0.5,0.975))
quant2 <- DRclass_lu_Quantile(sample_u,l=l,u=u,probs=c(0.025,0.5,0.975))

# plot selected features of the first component of the sample:
oldpar <- par(no.readonly=TRUE)
par(mar=c(5, 4, 1, 4) + 0.1)  # c(bottom, left, top, right)
plot(pdf1[1,,c("x","u")],type="l",xaxs="i",yaxs="i",xlim=c(-2,2),xlab="x",ylab="pdf")
lines(pdf2[1,,c("x","l")])
par(new=TRUE)
plot(cdf1[1,,c("x","F_upper")],type="l",xaxs="i",yaxs="i",axes=FALSE,
     xlim=c(-2,2),ylim=c(0,1),ylab="",lty="dashed")
axis(4); mtext("cdf",4,2)
lines(cdf2[1,,c("x","F_lower")],lty="dashed")
abline(v=quant1["quant_lower_0.5",1],lty="dotted")
abline(v=quant1["quant_upper_0.5",1],lty="dotted")
abline(v=quant1["quant_lower_0.025",1],lty="dotdash")
abline(v=quant1["quant_upper_0.975",1],lty="dotdash")
par(oldpar)

[Package DRclass version 0.1.0 Index]