DRclass_k_Cdf: Calculate lower and upper bounds of the cumulative density...

In DRclass: Consider Ambiguity in Probabilistic Descriptions Using Density Ratio Classes

Calculate lower and upper bounds of the cumulative density function for the marginals of a Density Ratio Class for which the lower and upper bounding functions are proportional.

Description

The cumulative density functions for the marginals of a distributions proportional to the lower and upper bounding functions are also provided.

Usage

DRclass_k_Cdf(sample_u, k = 1, 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.
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.

Details

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.

Value

Three dimensional array with the following dimensions: 1: variable corresponding to column of the sample 2: equidistant spacing of that variable 3: five columns for variable values, lower bound of the cdf of the marginal of the class, cdf of the marginal corresponding to the lower class boundary, cdf of the marginal corresponding to the upper class boundary, upper bound of the cdf of the marginal of the 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)

DRclass documentation built on April 3, 2025, 7:05 p.m.