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posterior

Class: gmdistribution

Posterior probabilities of components

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 fitgmdist. 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.

Examples

expand all

Compute Posterior Probabilities for Gaussian Mixture Variates

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

MU1 = [2 2];
SIGMA1 = [2 0; 0 1];
MU2 = [-2 -1];
SIGMA2 = [1 0; 0 1];
rng(1); % For reproducibility
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 = fitgmdist(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

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