Expectation Maximization On Old Faithful

Applies expectation maximization to fit a mixture of binomial distributions to a data set

ExpectationMaximizationOnOldFaithful applies Expectation Maximization to learn generating mixture of multi-nomial distributions for a 2D data set of waiting time between eruptions and the duration of the eruption for the Old Faithful geyser in Yellowstone National Park, Wyoming, USA.
USAGE: pauseSec is an optional parameter to add a delay after each iteration
ExpectationMaximizationOnOldFaithful() fits the dataset by two binormal distributions
ExpectationMaximizationOnOldFaithful( pauseSec, n) initializes expectation maximization with a multi-nomial distribution composed of n Gaussians, e.g. for 5:
>> ExpectationMaximizationOnOldFaithful( 0, 5)

ExpectationMaximizationOnOldFaithful(pauseSec, numGauss, theta)
initializes the algorithm with parameters theta, a struct with
- tau, a probaiity vector that a random data element belongs to each of n Gaussian distributions
- mu, the mean of each Gaussian distribution
- sigma, the covariance matrix for each Gaussian distributions

based on 'R' code by 3mta3 published on Wikipedia (http://en.wikipedia.org/wiki/Expectation–maximization_algorithm#mediaviewer/File:Em_old_faithful.gif)

Aaron T. Becker, 2015-03-01