{"articles":{"em-algorithm@computational-statistical-methods":{"content":"<p>\\[{f \\to{} X \\to{} Y = h(X)}\\] <br> Let \\(\\mathcal{M}\\) be a model with parameters \\(\\Theta\\), let \\({\\ell(\\theta\\vertX)}\\) be the log-likelihood function of the data. <br> What if some data is missing? Let \\(Y\\) be the available data and \\(Z\\) the missing data. The EM algorithm uses the available data Y and the immediate estimate \\(\\theta\\). E-step: we have the log-likelihood which depends on \\(\\theta\\), \\(Y\\) and \\(Z\\). We have \\(Y\\) and an approximation of \\(\\theta\\), but not \\(Z\\). In this step we sum out \\(Z\\) to create a function \\(Q\\) of \\(\\theta\\) and \\(Y\\) only. M-step: Maximize the function \\(Q\\) from the previous step to find a new estimate of the parameter \\(\\theta\\). <br> Start with an estimate of \\(\\theta\\). <ul></ul></p>","names":[[["EM algorithm",""]]]}},"style":"Method"}