A Bayesian mixture of K Gaussians is fitted to the standardised Old Faithful data by variational Bayes (Bishop 2006, Section 10.2): each iteration updates the responsibilities and the approximate posteriors q(π) and q(μk, Λk), and the lower bound L never decreases. Each ellipse is the one-standard-deviation contour of a component, shaded by its expected mixing coefficient E[πk]; components that explain almost no data fade and are dropped. Compare with maximum likelihood EM, which keeps every component, and with the bound across K.
Prior: m0 = 0, β0 = 1, W0 = I, ν0 = 2 on the standardised data, and Dirichlet(α0) for π. The start puts each component on one data point with unit covariance. Components credited with less than half a data point (Nk < 0.5) are not drawn. The update of νk is ν0 + Nk (the first printing of (10.63) has an extra + 1).
vbgmm_e_step, vbgmm_m_step, vbgmm_bound, fig10_6, fig10_7); this page uses the same updates and the same starting rows for preset 1.