Statistics Toolbox™

posterior - Posterior probabilities of components

Class

@gmdistribution

Syntax

P = posterior(obj,X)
[P,nlogl] = posterior(obj,X)

Description

P = posterior(obj,X) returns the posterior probabilities of each of the k components in the Gaussian mixture distribution defined by obj for each observation in the data matrix X. X is n-by-d, where n is the number of observations and d is the dimension of the data. obj is an object created by gmdistribution or fit. P is n-by-k, with P(I,J) the probability of component J given observation I.

posterior treats NaN values as missing data. Rows of X with NaN values are excluded from the computation.

[P,nlogl] = posterior(obj,X) also returns nlogl, the negative log-likelihood of the data.

Example

Generate data from a mixture of two bivariate Gaussian distributions using the mvnrnd function:

MU1 = [1 2];
SIGMA1 = [2 0; 0 .5];
MU2 = [-3 -5];
SIGMA2 = [1 0; 0 1];
X = [mvnrnd(MU1,SIGMA1,1000);mvnrnd(MU2,SIGMA2,1000)];

scatter(X(:,1),X(:,2),10,'.')
hold on

Fit a two-component Gaussian mixture model:

obj = gmdistribution.fit(X,2);
h = ezcontour(@(x,y)pdf(obj,[x y]),[-8 6],[-8 6]);

Compute posterior probabilities of the components:

P = posterior(obj,X);

delete(h)
scatter(X(:,1),X(:,2),10,P(:,1),'.')
hb = colorbar;
ylabel(hb,'Component 1 Probability')

See Also

gmdistribution, fit, cluster, mahal

polyval

prctile