Note as the results in (5.5.6) and (5.5.7) show that the conditional class prior for classes that are associated with observations other than yl is proportional to the number of such observations and that the combined prior for all other classes depends only on α and l'.
The main advantage of this representation is that it allows us to work with the finite
number of indicators cl, rather than the infinite number of mixing proportions, which is crucial for the estimation of this class of processes.
This shows that the conditional class prior for components that are associated with other observations is proportional to the number of such observations; the combined prior for all other classes depends only on α and n. Notice how the analytical tractability of the integral in eq. (12) is essential, since it allows us to work directly with the (finite number of) indicator variables, rather than the (infinite number of) mixing proportions.
Man beachte auch, dass die Gleichungen: 5.5.4 - 5.5.7, die vor der hier dokumentierten Stelle in der Dissertation zu finden sind, auch in der Quelle stehen.
Außerdem sei darauf hingewiesen, dass auf Seite 144 der Dissertation (vor dem Unterkapitel, das die hier dokumentierte Stelle enthält) folgender Satz steht: "The univariate development in Escobar and West (1995) and Rasmussen (2000) can be extended and modified to produce various methods of estimation described below."