DRclass_k_Quantile {DRclass} | R Documentation |
Calculate lower and upper bounds of quantiles of marginals of a Density Ratio Class for which the lower and upper bounding functions are proportional.
Description
Quantiles of the marginals of distributions proportional to the lower and upper bounding functions are also provided.
Usage
DRclass_k_Quantile(
sample_u,
k = 1,
probs = c(0.025, 0.25, 0.5, 0.75, 0.975),
tol = 0.001,
maxiter = 100
)
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 |
probs |
Vector of probabilities for which the quantile bounds are to be provided. |
tol |
Tolerance in quantile value for approximating the solution of the implicit equation for quantiles with the bisection algorithm. |
maxiter |
Maximum number of iterations for approximating the solution of the implicit equation for quantiles with the bisection algorithm. |
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
Matrix of quantile bounds and quantiles (rows) for different marginal variables (columns).
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)