credIntNum: Calculate a credible interval from a numerically specified...

In Bolstad2: Bolstad Functions

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

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

## 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)))

Bolstad2 documentation built on April 11, 2022, 5:08 p.m.