Page 304 - Computational Statistics Handbook with MATLAB

Chapter 8: Probability Density Estimation 293

figure
axis equal
axis(lim)
grid on
% Create and plot a circle for each term.
hold on
for i=1:nterm
% rescale for plotting purposes
ycord = scale*mix(i)+minx;
xc = mus(i)+sqrt(vars(i))*cos(t);
yc = ycord+sqrt(vars(i))*sin(t);
plot(xc,yc,mus(i),ycord,'*')
end
hold off
% Relabel the axis to show the right coefficient.
tick = (maxx-minx)/10;
set(gca,'Ytick',minx:tick:maxx)
set(gca,'XTick',minx:tick:maxx)
set(gc a,'YT ickLa bel', ...
'0|0.1|0.2|0.3|0.4|0.5|0.6|0.7|0.8|0.9|1')
xlabel('Means'),ylabel('Mixing Coefficients')
title('dF Plot for Univariate Finite Mixture')

The first circle on the left corresponds to the component with p i = 0.3 and
µ i = – 3. Similarly, the middle circle of Figure 8.13 represents the second
term of the model. Note that this representation of the mixture makes it easier
to see which terms carry more weight and where they are located in the
domain.

ii
ee
ii
Mult MultMult Multi ivvar vvarar ar i iaat aatt teeFini FiniFini Finit teeMixtuMixtu rees s
r
rr eess
MixtuMixtu
tt
ee
Finite mixtures is easily extended to the multivariate case. Here we define the
multivariate finite mixture model as the weighted sum of multivariate com-
ponent densities,
c
(
f x() = ∑ p g x; θ i . )
i
i = 1
As before, the mixing coefficients or weights must be nonnegative and sum
. When
to one, and the component density parameters are represented by θ i
we are estimating the function, we often use the multivariate normal as the
component density. This gives the following equation for an estimate of a
multivariate finite mixture
© 2002 by Chapman & Hall/CRC