Calculate a credible interval from a numerically specified posterior CDF

Description

Calculates a lower, upper, or two-sided credible interval from the numerical posterior CDF.

Usage

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credIntNum(theta, cdf, conf = 0.95, type="twosided")

Arguments

theta

the values over which the the posterior CDF is specified

cdf

the values of the CDF, F(θ) = \int_{-∞}^{θ}f(t).df where f(t) is the PDF.

conf

the desired 'confidence' level

type

the type of interval to return, 'lower' = one sided lower bound, 'two-sided' = two - sided, or 'upper' = one sided upper bound. It is sufficient to use 'l','t' or 'u'

Details

This function uses linear interpolation to calculate bounds for points that may not be specified by CDF

Value

a list containing the elements lower.bound, uppper.bound or both depending on type

Examples

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## commands for calculating a numerical posterior CDF.
## In this example, the likelihood is proportional to
## \eqn{\theta^{3/2}\times \exp(-\theta/4)} and a N(6, 9) prior is used.
theta <- seq(from = 0.001, to = 40, by = 0.001)
prior <- dnorm(theta,6,3)
ppnLike <- theta^1.5*exp(-theta/4)
ppnPost <- prior*ppnLike
scaleFactor <- sintegral(theta, ppnPost)$int
posterior <- ppnPost/scaleFactor
cdf <- sintegral(theta, posterior)$y
ci<-credIntNum(theta, cdf)
par(mfrow=c(2,2))
plot(prior ~ theta, type = 'l',  main = "Prior N(6, 9)")
plot(ppnLike ~ theta, type = 'l', main = "Proportional likelihood")
plot(posterior ~ theta, type = 'l', main = "Posterior")
abline(v=c(unlist(ci)))