% CONF2MAHAL - Translates a confidence interval to a Mahalanobis
% distance. Consider a multivariate Gaussian
% distribution of the form
%
% p(x) = 1/sqrt((2 * pi)^d * det(C)) * exp((-1/2) * MD(x, m, inv(C)))
%
% where MD(x, m, P) is the Mahalanobis distance from x
% to m under P:
%
% MD(x, m, P) = (x - m) * P * (x - m)'
%
% A particular Mahalanobis distance k identifies an
% ellipsoid centered at the mean of the distribution.
% The confidence interval associated with this ellipsoid
% is the probability mass enclosed by it. Similarly,
% a particular confidence interval uniquely determines
% an ellipsoid with a fixed Mahalanobis distance.
%
% If X is an d dimensional Gaussian-distributed vector,
% then the Mahalanobis distance of X is distributed
% according to the Chi-squared distribution with d
% degrees of freedom. Thus, the Mahalanobis distance is
% determined by evaluating the inverse cumulative
% distribution function of the chi squared distribution
% up to the confidence value.
%
% Usage:
%
% m = conf2mahal(c, d);
%
% Inputs:
%
% c - the confidence interval
% d - the number of dimensions of the Gaussian distribution
%
% Outputs:
%
% m - the Mahalanobis radius of the ellipsoid enclosing the
% fraction c of the distribution's probability mass
%
% See also: MAHAL2CONF
% Copyright (C) 2002 Mark A. Paskin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function m = conf2mahal(c, d)
m = chi2inv(c, d);
% pr = 0.95 ; c = (1 - pr)/2 ;
% m = norminv([c 1-c],0,1) ;