fabzCI.RdComputation of a 1-alpha FAB z-interval
fabzCI(y, mu, t2, s2, alpha = 0.05)
| y | a numeric scalar |
|---|---|
| mu | a numeric scalar |
| t2 | a positive numeric scalar |
| s2 | a positive numeric scalar |
| alpha | the type I error rate, so 1-alpha is the coverage rate |
a two-dimensional vector of the left and right endpoints of the interval
A FAB interval is the "frequentist" interval procedure
that is Bayes optimal: It minimizes the prior expected
interval width among all interval procedures with
exact 1-alpha frequentist coverage. This function computes
the FAB z-interval for the mean of a normal population with an
known variance, given a user-specified prior distribution
determined by psi. The prior is that the population mean
is normally distributed.
Referring to the elements of psi
as mu, t2, s2, the prior and population variance are
determined as follows:
mu is the prior expectation of the mean
t2 is the prior variance of the mean
s2 is the population variance
Peter Hoff
y<-0 fabzCI(y,0,10,1)#> [1] -1.810617 1.810617fabzCI(y,0,1/10,1)#> [1] -1.644915 1.644976fabzCI(y,2,10,1)#> [1] -1.716378 1.963615fabzCI(y,0,1/10,1)#> [1] -1.644915 1.644976