Bayesian Statistics: An Introduction, 4th Edition

9.2 The EM algorithm

9.2.1 The idea of the EM algorithm

A useful numerical technique which finds the posterior mode, that is, the value at which or equivalently is a maximum, but does not provide full information on the posterior distribution is the EM algorithm. We can exemplify this by an example on genetic linkage due to Rao (1973, Section 5g) quoted by Dempster et al. (1977), by Gelfand and Smith (1990) and by Tanner (1996, Section 4.1). We have observations with cell probabilities

and we want to estimate η. The likelihood is then

What we do is to augment the data by adding further data to produce augmented data . It should be noted that to a considerable extent the distinction between ...