A mixture model can be represented using a Bayesian network as shown in the network
diagram above. The model shown here was learnt using the continuous variables {Sepal
Length, Sepal Width, Petal Length and Petal Width} from the well known
Iris data set. The Bayes Server network file for this model can be found
here.
This interactive demo charts the joint distribution of Petal Length and Petal Width,
i.e. P(Petal length, Petal width), calculated using the Bayes Server API before
evidence (Gray) and given evidence (Red). It also calculates the log likelihood
of evidence entered and the posterior Cluster probabilities.
This is an example of multivariate modelling. In this simple example we are updating
our beliefs about the joint distribution of Petal length and Petal width given what
we know (evidence) about other variables.
The discrete cluster variable (mixture component) allows us to model more complex
distributions by combining simpler distributions each with different importance
(weight).