% Posterior probability interval of the balanced accuracy.
%
% Usage:
% [b_lower,b_upper] = bacc_ppi(C,alpha)
%
% Arguments:
% C - 2x2 confusion matrix of classification outcomes. This matrix
% needs to be of the form C = [a b; c d] where
% <a> is the number of true positives
% <b> is the number of false negatives
% <c> is the number of false positives
% <d> is the number of true negatives
% In other words: rows are true classes, columns are estimated
% classes.
% alpha - The posterior probability interval will cover 1-alpha of
% probability mass such that (1-alpha)/2 remains on either end of
% the distribution.
%
% Example:
% C = [90, 10; 5 95];
% alpha = 0.05;
% [b_lower,b_upper] = bacc_ci(C,alpha);
%
% Literature:
% K.H. Brodersen, C.S. Ong, K.E. Stephan, J.M. Buhmann (2010).
% The balanced accuracy and its posterior distribution. In: Proceedings
% of the 20th International Conference on Pattern Recognition.
% Kay H. Brodersen, ETH Zurich, Switzerland
% http://people.inf.ethz.ch/bkay/
% $Id: bacc_ppi.m 8245 2010-10-22 12:57:51Z bkay $
% -------------------------------------------------------------------------
function [b_lower,b_upper] = bacc_ppi(C,alpha)
A1 = C(1,1) + 1;
B1 = C(1,2) + 1;
A2 = C(2,2) + 1;
B2 = C(2,1) + 1;
b_lower = betaavginv(alpha/2,A1,B1,A2,B2);
b_upper = betaavginv(1-alpha/2,A1,B1,A2,B2);
end