**6. Conclusions**

The problem of choice of the number of principal components to use to represent a complex of variables—a multivariate sample—has been considered in this chapter.

In addition to some *ad hoc* arithmetic criteria, Akaike's information criterion (AIC) and the Bayesian information criterion (BIC) have been applied here to the choice of the number of principal components to represent a dataset. The results have been compared and contrasted with *ad hoc* criteria such as retaining those principal components that explain more than an average amount of the total variance. The use of BIC is seen to correspond rather closely to the rule of retaining PCs whose eigenvalues are larger than average.
