pNull {Bolstad2}R Documentation

Test a one sided hypothesis from a numerically specified posterior CDF or from a sample from the posterior


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


pNull(theta0, theta, cdf = NULL, type = 'upper')



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


a sample of values from the posterior density, or, if cdf is not NULL then the values over which the the posterior CDF is specified


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


the type of probability to return, 'lower' = Pr(theta <= theta0) or 'upper' = Pr(theta >= theta0). It is sufficient to use 'l' or 'u'


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


a list containing the element prob which will be the upper or lower tail probability depending on type


## 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
pNull(15, theta, cdf)

## Use an inverse method to take a random sample of size 1000
## from the posterior
suppressWarnings(Finv <- approxfun(cdf, theta))
pNull(15, thetaSample)

[Package Bolstad2 version 1.0-28 Index]