 Finite Gaussian mixture with a common variance

A finite Gaussian mixture with a common variance has density $f(y)={\sum }_{j=1}^k{\pi }_j\varphi (y;{\mu }_j,{\sigma }^2)$, with positive common variance and weights summing to one. The means locate its latent components, which need not correspond to distinct modes. It has $2k$ free parameters: $k-1$ weights, $k$ means and one variance. EM for Gaussian mixtures with a common variance supplies iterative likelihood updates.