An instance crucial. to most problems in signal processing is the sele
ction of the order of a presupposed model. Examples are the determinat
ion of the putative number of signals present in white Gaussian noise
or the number of noise-contaminated sources impinging on a passive sen
sor array. It is shown that maximum a posteriori Bayesian arguments, c
oupled with maximum entropy considerations, offer an operational and c
onsistent model order selection scheme, competitive with the minimum d
escription length criterion.