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 ...
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