Abstract
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 language | English |
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Pages (from-to) | 99-107 |
Number of pages | 9 |
Journal | Pattern Recognition |
Volume | 9 |
Issue number | 2 |
DOIs | |
State | Published - Jul 1977 |
Externally published | Yes |
Keywords
- Bayesian theory
- Binary features
- Pattern recognition classification
- Posterior probabilities
- Probability of error