Properties and convergence of a posteriori probabilities in classification problems

Moshe Ben-Bassat, Shmuel Gal

Research output: Contribution to journalArticlepeer-review


This report investigates the behavior of the a posteriori probabilities for classification problems in which the observations are not identically distributed. Some basic properties of the a posteriori probabilities are presented; then, it is shown that for each class the a posteriori probability converges a.s. to a random variable. Conditions are given for a.s. convergence of the a posteriori probability to 1 for the true class (and to 0 for all other classes). The results are illustrated for the case of two classes and binary observations, and finally a numerical example is presented.

Original languageEnglish
Pages (from-to)99-107
Number of pages9
JournalPattern Recognition
Issue number2
StatePublished - Jul 1977
Externally publishedYes


  • Bayesian theory
  • Binary features
  • Pattern recognition classification
  • Posterior probabilities
  • Probability of error

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


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