% belicitor.m
% Elicits a beta prior with the mean "mn" in (0,1)
% and with a "withprob" quantile equal to "quant".
% It solves a nonlinear equation involving betainc,
% since quantiles of beta are not explicit.
% given E theta=0.8, P(theta < 0.9) = 0.95.
mn= 0.8
quant = 0.9;
withprob = 0.95;
fun = @(alpha) betainv(quant, alpha, alpha * (1 - mn)/mn )- withprob
%
alph = fsolve( @(alpha)fun(alpha), 1)
bet = alph * (1 - mn)/mn
%
% % alph = 6.5087
% % bet = 1.6272
% % The prior is (approx) B(6.5, 1.6).
%