Bolstad2 (version 1.0-29)

credInt: Calculate a credible interval from a numerically specified posterior CDF or from a sample from the posterior

Description

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

Usage

credInt(theta, cdf = NULL, conf = 0.95, type = "twosided")

Arguments

theta

either a sample from the posterior density or the values over which the the posterior CDF is specified

cdf

the values of the CDF, \(F(\theta) = \int_{-\infty}^{\theta}f(t).df\) where \(f(t)\) is the PDF. This only needs to be specified if a numerically specified posterior is being used

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'

Value

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

Details

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

Examples

# NOT RUN {
## 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 = credInt(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)))

## Use an inverse method to take a random sample of size 1000
## from the posterior
suppressWarnings({Finv = approxfun(cdf,theta)})
thetaSample = Finv(runif(1000))
ci = credInt(thetaSample)

# }