solbeta: Recursive resolution of beta prior calibration
Description
In the capture-recapture experiment of Chapter 5, the prior information
is represented by a prior expectation and prior confidence intervals. This
function derives the corresponding beta $B(\alpha,\beta)$
prior distribution by a divide-and-conquer scheme.
Usage
solbeta(a, b, c, prec = 10^(-3))
Arguments
a
lower bound of the prior 95%~confidence interval
b
upper bound of the prior 95%~confidence interval
c
mean of the prior distribution
prec
maximal precision on the beta coefficient $\alpha$
Value
alphafirst coefficient of the beta distribution
betasecond coefficient of the beta distribution
Details
Since the mean $\mu$ of the beta distribution is known, there is a single free parameter
$\alpha$ to determine, since $\beta=\alpha(1-\mu)/\mu$. The function solbeta searches for
the corresponding value of $\alpha$, starting with a precision of $1$ and stopping
at the requested precision prec.