pnullNum {Bolstad2}

Test a one sided hypothesis from a numerically specified posterior CDF

Description

Calculates the probability of a one sided null hypothesis from a numerically calculated posterior CDF.

Usage

pnullNum(theta0, theta, cdf, type = "upper")

Arguments

theta0

the hypothesized value, i.e. H0: theta <= theta0

theta

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.

type

the type of probability to return, 'lower' = Pr(theta <= theta0) or 'upper' = Pr(theta >= theta0). It is sufficient to use 'l' 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 element prob which will be the upper or lower tail probability 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
pnullNum(1, theta, cdf)