diff toolboxes/FullBNT-1.0.7/KPMtools/conf2mahal.m @ 0:e9a9cd732c1e tip

first hg version after svn

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+++ b/toolboxes/FullBNT-1.0.7/KPMtools/conf2mahal.m	Tue Feb 10 15:05:51 2015 +0000
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+% 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
+%
+% This program is free software; you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation; either version 2 of the License, or
+% (at your option) any later version.
+%
+% This program is distributed in the hope that it will be useful, but
+% WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+% General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this program; if not, write to the Free Software
+% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
+% USA.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function m = conf2mahal(c, d)
+
+m = chi2inv(c, d);
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