SUMMARY

Scheinok’s (1972) empirical results, obtained from using Bahadur’s expansion in Bayes’s theorem, are explained by noting that the expansion is an exact representation of observed probabilities and thus no information was gained by its use. The calcu-lated and observed joint probability distributions will always be equal. It is also demonstrated that posterior probabilities equal to the ratio of observed patients with a givenprofile in a disease category to the totalnumber ofpatients with thesymptomprofile are always obtained when actuarial probability estimates are used in Bayes’s theorem. SOMMAIRE Les resultats empiriques de Scheinok obtenus grdce a la variante de Bahadur du theoreme de Bayes s’expliquent par le fait que cette variante donne une representation exacte des probabilites observees et que son usage ne permet pas de gagner de I’information. Les distributions de probabi1itP.s qu’elles soient observees ou calculees restant toujours d peu pres identiques. On demontre egalement que des probabilites a posteriori, egales au rapport du nombre de patients ayant un profil de symptomes et une maiadie don&s au nombre total depatients ayant ce proj2, sont toujours obtenues quand on utilise dans la formule de Bayes des estimations calculees de probabilites. Bahadur (1961) has derived an exact finite series representation for the general multinomial model. Scheinok (1972) has considered its use in a diagnostic context. Since both authors present detailed discussion of the expansion, its derivation will not be considered here, except to point out that P*(X), the distribution under dependence, is not, in the general case, an approximation based on underlyin