Properties and convergence of a posteriori probabilities in classification problems

Moshe Ben-Bassat; Shmuel Gal

doi:10.1016/0031-3203(77)90021-8

Properties and convergence of a posteriori probabilities in classification problems

Moshe Ben-Bassat, Shmuel Gal

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	99-107
Number of pages	9
Journal	Pattern Recognition
Volume	9
Issue number	2
DOIs	https://doi.org/10.1016/0031-3203(77)90021-8
State	Published - Jul 1977
Externally published	Yes

Keywords

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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10.1016/0031-3203(77)90021-8

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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.",

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author = "Moshe Ben-Bassat and Shmuel Gal",

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AU - Gal, Shmuel

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AB - 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.

KW - Bayesian theory

KW - Binary features

KW - Pattern recognition classification

KW - Posterior probabilities

KW - Probability of error

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ER -

Properties and convergence of a posteriori probabilities in classification problems

Abstract

Keywords

ASJC Scopus subject areas

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