| BAYESERR | |
Bayesian risk for 1D Gaussians and 0/1-loss.
Synopsis:
[risk,eps1,eps2,inter1] = bayeserr(model)
Description:
This function computes Bayesian risk of a classifier
with the following assumptions:
- 1/0 loss function (risk = expectation of misclassification).
- Binary classification.
- Class conditional probabilities are univariate Gaussians.
Input:
model [struct] Mixture of two univariate Gaussians.
.Mean [1x2] Mean values [Mean1 Mean2].
.Cov [1x2] Covariances [Cov1 Cov2].
.Prior [1x2] A priory probabilities.
Output:
risk [1x1] Bayesian risk for an optimal classifier.
eps1 [1x1] Integral of p(x|k=1) over x in L2, where
L2 is the area where x is classified to the 2nd class.
eps2 [1x1] Integral of p(x|k=2) over x in L1, where
L1 is the area where x is classified to the 1st class.
inter1 [1x2] or [1x4] One or two intervals describing L1.
Example:
model = struct('Mean',[0 0],'Cov',[1 0.4],'Prior',[0.4 0.6]);
figure; hold on;
h = pgmm(model,struct('comp_color',['r' 'g']));
legend(h,'P(x)','P(x|y=1)*P(y=1)','P(x|y=2)*P(y=2)');
[risk,eps1,eps2,interval] = bayeserr(model)
a = axis;
plot([interval(2) interval(2)],[a(3) a(4)],'k');
plot([interval(3) interval(3)],[a(3) a(4)],'k');
See also
BAYESDF, BAYESCLS
About: Statistical Pattern Recognition Toolbox
(C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac
Czech Technical University Prague
Faculty of Electrical Engineering
Center for Machine Perception
Modifications:
22-oct-2009, VF, fixed bug on line 157; bug reported 2009-10-08 by krejci.filip@gmail.com
20-mar-2006, VF, A mistake in help removed; bug reported by O. Sychrovksy.
02-may-2004, VF
19-sep-2003, VF
27-Oct-2001, VF