DRclass (version 0.1.0)

DRclass_k_Pdf: Calculate marginal class bounding functions for a special Density Ratio Class for which the lower and upper bounding functions are proportional.

Description

This function is more efficient than 'DRclass_lu_Pdf' as it does not need the evaluation of the bounding functions, l and u. It is thus recommended to use this function if l and u are proportional.

Usage

DRclass_k_Pdf(sample_u, k = 1, nout = 512, ...)

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

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.

k

Factor of proportionality between upper (u) and lower (l) bound: u = k * l

nout

Number of equally spaced output intervals for the marginal densities.

...

Further arguments passed to the function 'density'

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)